Question

If using the method of completing the square to solve the quadratic equation

x2 – 9x + 38 0, which number would have to be added to "complete the
square"?
=

Answer 1

81/4

Explanation:

Given the equation x^2 – 9x + 38 = 0

Subtract 38 from both sides

x^2 – 9x + 38 - 38= 0 - 38

x^2 - 9x = -38

Next is to complete the square, to do this we will add the square of the half of coefficient of x to both sides as shown;

Coefficient of x is - 9

Half of -9 will be (-9/2)

Squaring the result will give (-9/2)² = 81/4

Hence the number that would have to be added to "complete the

square" is 81/4 to have;

x^2 - 9x + 81/4= -38 + 81/4

(x-9/2)² = -38 + 81/4

Hence the required value is 81/4