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20 Cards in this Set
- Front
- Back
- 3rd side (hint)
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(x-2)(x+3) = 0
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x= 2 or x= -3
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If (x-2)(x+3) = 0, then either
x-2= 0 or x+3 = 0 |
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x² = 4 for x
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x= -2 or x= 2
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x²-4 = 0
(x+2)(x-2) = 0 x+2 = 0 or x-2 = 0 |
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What is the quadratic formula?
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x= -b ± √(b² - 4ac)
-------------------- 2a |
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2x² - x- 21 = 0
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7/2 or -3
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Step 1
-b ± √(b² - 4ac) -------------------- 2a a=2, b= -1 and c= -21 Step 2- -(-1) ±√ {(-1)² - (4)2(-21)} ---------------------------------- 2(2) Step 3- 1 ± √ (1 + 168) ---------------------- 4 Step 4- 1 ± 13 --------- 4 Step 5- 1 ± 13 --------- 4 OR 1 - 13 --------- 4 |
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In the quadratic equation 5x² - x + 9, find the values of a,b, and c.
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a= 5
b= -1 c- 9 |
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Solve x² + 5x - 14= 0 using the quadratic formula.
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2 or -7
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Step 1-
-5 ± √{5²- 4(1)(-14) -------------------------- 2(1) Step 2- -5 ± √(25 + 56) --------------------- 2 Step 3- -5 ± √81 ------------- 2 Step 4- -5 ± 9 --------- 2 Step 5- -5 +9 --------- 2 OR -5 - 9 -------- 2 |
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Solve 2x² = x + 21 by using the quadratic formula.
First write equation in the correct form. 2x² - x - 21 = 0 |
7/2 or -3
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Step 1-
-(-1) ± √{ (-1)² - 4(2)(-21) } ---------------------------------- 2(2) Step 2- 1 ± √(1 +68) ------------------ 4 Step 3- 1 ± √169 ------------- 4 Step 4- 1 ± 13 --------- 4 Step 5- 1 + 13 ---------- 4 OR 1 - 13 --------- 4 |
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Solve 3x² + x - 5 = 0
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1.14 or -1.47
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Step 1-
-1 ± √{ 1² - (4)(3)(-5) } ----------------------------- 2(3) Step 2- -1 ± √(1 +60) ------------------- 6 Step 3- -1 ± √61 ------------ 6 Step 4- -1 ± 7.81 ------------- 6 Step 5- -1 + 7.81 ------------- 6 OR -1 - 7.81 ------------ 6 Step 6- 6.81 ------- 6 OR -8.81 ------- 6 |
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x² + x - 6 = 0
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2 or -3
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Step 1-
-1 ± √{1² - (4)(1)(-6) -------------------------- 2(1) Step 2- -1 ± √25 ----------- 2 Step 3- -1 ± 5 --------- 2 Step 4- -1 + 5 --------- 2 OR -1 - 5 --------- 2 Step 5- 4 -- 2 OR -6 --- 2 |
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x² - 4x - 21 = 0
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7 or -3
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Step 1-
-(-4) ± √{-4² - 4(1)(-21) } -------------------------------- 2(1) Step 2- 4 ± √(16 + 84) -------------------- 2 Step 3- 4 ± √100 ------------- 2 Step 4- 4 ± 10 -------- 2 Step 5- 4 + 10 ---------- 2 OR 4 - 10 --------- 2 Step 6- 14 ---- 2 OR -6 --- 2 |
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x² + 8x - 9 = 0
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1 or -9
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Step 1-
-8 ± √{8² - (4)(1)(-9) } ----------------------------- 2(1) Step 2- -8 ± √100 -------------- 2 Step 3- -8 ± 10 ---------- 2 Step 4- -8 + 10 ----------- 2 OR -8 - 10 ----------- 2 Step 5- 2 -- 2 OR -18 ----- 2 |
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5x² + 2x = 0
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0 or -2/5
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Step 1-
-2 ± √{2² - (4)(5)(0) } ---------------------------- 2(5) Step 2- -2 ± √4 ---------- 10 Step 3- -2 ± 2 --------- 10 Step 4- -2 + 2 --------- 10 OR -2 - 2 -------- 10 Step 5- 0 ---- 10 OR -4 ----- 10 |
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2x² - 4x - 21 = 0
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4.4 or -2.4
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Step 1-
-(-4) ± √{-4² - (4)(2)(-21) } ----------------------------------- 2(2) Step 2- 4 ± √184 ------------- 4 Step 3- 4 ± 13.6 ------------ 4 Step 4- 4 +13.6 ---------- 4 OR 4 - 13.6 ------------ 4 Step 5- 17.6 ------- 4 OR -9.6 ------- 4 |
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48x² - 32x - 35 = 0
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1.25 aka 5/4
or -0.58 aka -7/12 |
Step 1-
-(-32) ± √{-32² -(4)(28)(-35)} --------------------------------------- 2(48) Step 2- 32 ± √7744 ---------------- 96 Step 3- 32 ± 88 ----------- 96 Step 4- 32 + 88 ------------ 96 OR 32 - 88 ---------- 96 Step 5- 120 ------ 96 OR -56 ------ 96 |
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2x² + 5x - 12 = 0
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3/2 or -4
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Step 1-
-5 ± √{5² - (4)(2)(-12)} -------------------------------- 2(2) Step 2- -5 ± √121 --------------- 4 Step 3- -5 ± 11 ------------ 4 Step 4- -5 + 11 ---------- 4 OR -5 - 11 ---------- 4 Step 5- 6 -- 4 OR -16 ----- 4 |
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3x² - 75 = 0
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5
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Step 1-
-0 ± √{0² - (4)(3)(-75) ------------------------------ 2(3) Step 2- 0 ± √900 ------------- 6 Step 3- 30 ---- 6 |
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13x² +178x - 56 = 0
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-14 or 4/13
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Step 1-
-178 ± √{178² - (4)(12)(-56) } ----------------------------------------- 2(13) Step 2- -178 ± √(34596 ----------------------- 26 Step 3- -178 + 186 ---------------- 26 OR -178 - 186 --------------- 26 Step 4- 8 --- 26 OR -364 ------- 26 |
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3x² = 17
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2.38
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Step 1-
3x² - 17 = 0 Step 2- -0 ± √{0² - (4)(3)(-17)} ------------------------------ 2(30 Step 3- √204 -------- 6 Step 4- 14.3 ------- 6 |
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x² + x = 1
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1/2 or -3/2
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Step 1-
x² + x - 1 = 0 Step 2- -1 ± √{1² - (4)(1)(-1)} ---------------------------- 2(1) Step 3- -1 ± √4 ----------- 2 Step 4- -1 ± 2 --------- 2 Step 5- -1 + 2 ---------- 2 OR -1 - 2 --------- 2 |
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5x² + 3x = 0
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0 or -3/5
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Step 1-
-3 ± √{3² - (4)(5)(0)} --------------------------- 2(5) Step 2- -3± √9 --------- 10 Step 3- -3 ± 3 --------- 10 Step 4- -3 + 3 --------- 10 OR -3 - 3 -------- 10 Step 5- 0 -- 10 OR -6 ---- 10 |
