Question

Let ​

x^2−12x=61
.​
What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.

​
x2−12x+_____=______

​

Answer 1

Explanation:

Add the square of half the x-coefficient to both sides.

x² -12x +(-6)² = 61 +(-6)²

x² -12x +36 = 97

Answer 2

x² - 12x + 36 = 97

Explanation:

Given

x² - 12x = 61

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(- 6)x + (- 6)² = 61 + (- 6)², so

x² - 12x + 36 = 61 + 36

x² - 12x + 36 = 97