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

Blank 1: 36
Blank 2: 61
You could also change this into vertex form by making it y=(x-6)^2 -61

Answer 2

We have been given a quadratic equation $x^{2}-12x=61$  and we have  to complete the square of the given equation.

We know that a perfect square is in form of  $a^{2}+2ab+b^{2}$. Comparing the given equation we can see that $a^{2}$ in case is equal to $x^{2}$ and 2ab equals to -12x.

Now we have to figure what $b^{2}$ we should add to our equation to get a perfect square.

Since we know we can complete the square by taking half of coefficient of x term and squaring it.

Coefficient of x in our equation is 12 so to get  $b^{2}$  of our equation we have to divide it by 2. After dividing by 2 we will get 6 and now we will take square of 6.

$6^{2}=36$

Now we have to add 36 to both sides of our equation to hold our original equation true.

$x^{2}-12x+36=61+36\\ x^{2}-12x+36=97$

So we have to fill in the given space 36 to left hand side of equation and 97 to right hand side of equation.