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

Question

Question

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

in progress 0

Mathematics Neala 5 years 2021-08-19T02:22:45+00:00 2021-08-19T02:22:45+00:00 1 Answers 26 views 0

Answers ( )

Name*

E-Mail*

Website

Featured image

Browse

Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

Answer*

Helga · Answer 1 · 2021-08-19T02:24:13+00:00

Given:

The equation is:

$x^2-10x=7$

To find:

The number that should be added to sides of the equation to complete the square.

Solution:

If an expression is in the form of $x^2+bx$ , then we have to add $\left(\dfrac{b}{2}\right)^2$ to make it perfect square.

We have,

$x^2-10x=7$ …(i)

To make it perfect square we need to add square of half of coefficient of x on both sides.

Coefficient of x is -10, so square of half of coefficient of x is:

$\left(\dfrac{-10}{2}\right)^2=(-5)^2$

$\left(\dfrac{-10}{2}\right)^2=25$

On adding 25 on both sides of (i), we get

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

$(x-5)^2=32$

Therefore, we need to add 25 to both sides of the equation to complete the square.