Question

Complete the square for each expression. Then factor the Trinomial x^2+8x

Answer 1

The value of x is $x=0$ or $x=-8$

Step-by-step explanation:

The expression is $x^{2} +8x=0$

To complete the square, the equation is of the form $ax^{2} +bx+c=0$

The constant term c can be determined using, $c=\left(\frac{\frac{b}{a}}{2}\right)^{2}$

$\begin{aligned}c &=\left(\frac{8}{2}\right)^{2} \\&=\left(\frac{8}{2}\right)^{2} \\c &=4^{2} \\c &=16\end{aligned}$

Rewriting the expression $x^{2} +8x=0$ and factoring the trinomial, we have,

$\begin{array}{r}{x^{2}+8 x+16=16} \\{(x+4)^{2}=16}\end{array}$

Taking square root on both sides, we get,

$\begin{aligned}&x+4=\sqrt{16}\\&x+4=\pm 4\end{aligned}$

Either,

$\begin{array}{r}{x+4=4} \\{x=0}\end{array}$  or $\begin{array}{r}{x+4=-4} \\{x=-8}\end{array}$

Thus, the value of x is  $x=0$ or $x=-8$