Question

Solve each equation by factoring, and state the solutions.

Answer 1

Answer:

(a) $x^2+25=(x-5)^2+2\times x\times 5=(x-5)^2+10x$

(b) x = -5, -5

Step-by-step 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 $x^2+25=(x-5)^2+2\times x\times 5=(x-5)^2+10x$

(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