Question

Let ​ x2−12x=61 .​ What values make an equivalent number sentence after completing the square? Enter your answers in the boxes. ​ x2−12x+_____ ​= ​______

Answer 1

The answer for the first blank is 36 and the answer for the second blank is 97.
To complete the square, we first take half of the value of b. The value of b in this equation is -12; -12/2 = -6.
Next we square the value we just got: (-6)² = 36.
This is what we add to both sides of the equation, giving us:x²-12x+36=61+36
Combining like terms on the right, we havex²-12x+36=97

Answer 2

Add the square of half the x-coefficient to both sides.
x² -12x +(-6)² = 61 +(-6)²
x² -12x +36 = 97