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.