Question

Find the values if a and b such that x squared + 2x -7 = (x+a) squared + b​

Answer 1

Given:

$x^2+2x-7=(x+a)^2+b$

To find:

The values of a and b.

Solution:

We have,

$x^2+2x-7=(x+a)^2+b$

It can be written as

$(x^2+2x)-7=(x+a)^2+b$

Add and subtract square of half of coefficient of x in the parenthesis.

$(x^2+2x+(\dfrac{2}{2})^2-(\dfrac{2}{2})^2)-7=(x+a)^2+b$

$(x^2+2x+1^2)-1-7=(x+a)^2+b$

$(x+1)^2-8=(x+a)^2+b$     $[\because (x+y)^2=x^2+2xy+y^2]$

$(x+1)^2+(-8)=(x+a)^2+b$

On comparing both sides, we get

$a=1$

$b=-8$

Therefore, the value of a is 1 and the value of b is -8.