Question

Find the term that must be added to the equation x2−6x=7 to make it into a perfect square.

Answer 1

x²-6x =7

First we have get rid of that 7 from the right side and move it to the left side. To move 7 to the left side, we have to subtract 7 from both sides.

x²-6x-7= 7-7

x²-6x-7 = 0

To make this equation a perfect square, first we have to check the x term. Here -6x given. We have to divide the co-efficient of x by 2, and then we have to add the square of it.

The co-efficient of x is -6 here. Dividing it by 2, we will get -6/2 = -3.

We will have to add (-3)² here. (-3)² is 9. So in the place of -7, we have to make 9, to make the equation a perfect square.

9-(-7) = 9+7 = 16

So by adding 16 to the left side, we can make the equation a perfect square.

x²-6x-7+16 =0

x²-6x+9 =0

x²-6x+(-3)² =0

(x-3)² =0