Question

What number should be added to both sides of the equation to complete the square? x2 – 10x = 7

Answer 1

You take half the coefficient of the x term and then square it and then add it to both sides.
$x^2- 10x = 7$
$(x^2-10x +25)=7+25[$$(x^2-10x +25)=32$ 
$(x-5)^2=32$
In your case, 25 should be added to both sides complete the square

Answer 2

we have

$x^{2} -10x=7$

Complete the square. Remember to balance the equation by adding the same constants to each side

to complete the square adds $(10/2)^{2}=25$ both sides

so

$x^{2} -10x+25=7+25$

$x^{2} -10x+25=32$

Rewrite as perfect squares

$(x-5)^{2}=32$

Square root both sides

$x-5=(+/-)\sqrt{32}$

$x=5(+/-)\sqrt{32}$

$x1=5+\sqrt{32}$

$x2=5-\sqrt{32}$

therefore

the answer is

The number is $25$