In math, completing the square only works with quadratic functions, otherwise the equation will not be able to solve.
An important rule to understand when deriving the quadratic formula by completing the square, is that the leading term must equal to “1”. On the other hand, if the leading term does not equal to “1”, one will have to factor the equation by dividing each term by the leading term.
The quadratic equation must start as the following: 〖ax〗^2+bx+c=0. Next, the constant number is to be moved to the other side of the equation. Another important rule in math is that whenever a number is moved, the sign changes. In this case the constant “c” is positive, and later changed as “-c” when moved to the right side of the equation. As a result, it should look like the …show more content…
The following formula represents the quadratic formula:x=(-b±√(b^2-4ac))/2a After plugging each number to their corresponding term, it must first look like the following x=(-(-1)±√(〖(-1)〗^2-4(2)(2)))/(2(2))Next “-1” is multiplied by a negative which equals to a positive “1”. Moreover, the discriminant must be simplified and equal to √(1-16) which equals to √(-15). In math, a square root must never be negative, so an “i” which stands for imaginary number will replace the negative sign and cancel out the square root. Now the quadratic formula looks like the following: x=(1±√(-15))/(2(2)). Then, the denominator is simplified by multiplying “2” times “2” which equals to “4”. Finally, the quadratic formula now looks like the following: x=(1±√(-15))/4. Since both have the same denominator, the last step will be to separate the solution. This means that the equation has two complex with conjugate solutions. In other words, one solution is positive and the other is negative: x=(1+√(-15))/4 and
An important rule to understand when deriving the quadratic formula by completing the square, is that the leading term must equal to “1”. On the other hand, if the leading term does not equal to “1”, one will have to factor the equation by dividing each term by the leading term.
The quadratic equation must start as the following: 〖ax〗^2+bx+c=0. Next, the constant number is to be moved to the other side of the equation. Another important rule in math is that whenever a number is moved, the sign changes. In this case the constant “c” is positive, and later changed as “-c” when moved to the right side of the equation. As a result, it should look like the …show more content…
The following formula represents the quadratic formula:x=(-b±√(b^2-4ac))/2a After plugging each number to their corresponding term, it must first look like the following x=(-(-1)±√(〖(-1)〗^2-4(2)(2)))/(2(2))Next “-1” is multiplied by a negative which equals to a positive “1”. Moreover, the discriminant must be simplified and equal to √(1-16) which equals to √(-15). In math, a square root must never be negative, so an “i” which stands for imaginary number will replace the negative sign and cancel out the square root. Now the quadratic formula looks like the following: x=(1±√(-15))/(2(2)). Then, the denominator is simplified by multiplying “2” times “2” which equals to “4”. Finally, the quadratic formula now looks like the following: x=(1±√(-15))/4. Since both have the same denominator, the last step will be to separate the solution. This means that the equation has two complex with conjugate solutions. In other words, one solution is positive and the other is negative: x=(1+√(-15))/4 and