Question

Solve each equation by factoring, and state the solutions.

a. x^2 + 25 = 0
b. x^2 + 10x + 25 = 0

Answer 1

(a)
`x^2+25=(x-5)^2+2* x* 5=(x-5)^2+10x`

(b) x = -5, -5

Explanation:

We have given that the equation

(a)
`x^2+25=0`

We have to factorize the equation

We know that
`(a-b)^2=a^2+b^2-2ab`

So
`(a-b)^2+2ab=a^2+b^2`

So
`x^2+25=(x-5)^2+2* x* 5=(x-5)^2+10x`

(B) We have given equation
`x^2+10x+25`

It can be factorize as
`x^2+10x+25=x^2+5x+5x+25=x(x+5)+5(x+5)`

Now taking x+5 as common

`(x+5)(x+5)` = 0

x= -5 , -5