Question

Let x^2 - 12x=61

What values make an equivalent number sentence after completing the square?

Enter your answers in the boxes.

x^2- 12x +___=___

Answer 1

The given expression is:


`x^(2) -12x=61 \\ \\ x^(2) -2(x)(6)=61`

The general formula of square of difference of two numbers is:

(a - b)² = a² - 2ab + b²

Comparing the given equation to above equation, we can say, on the left hand side of the given equation, we have the square of first term and twice the product of first and second term. So what is missing is the square of second term. Adding square of second term on both sides of the equation we get:


`x^(2) -2(x)(6)+6^(2) =61+6^(2) \\ \\ x^(2) -12x+36=97`

So, 36 and 97 will be the answer to the given blanks.