The value of x is [tex]x=0[/tex] or [tex]x=-8[/tex]
Step-by-step explanation:
The expression is [tex]x^{2} +8x=0[/tex]
To complete the square, the equation is of the form [tex]ax^{2} +bx+c=0[/tex]
The constant term c can be determined using, [tex]c=\left(\frac{\frac{b}{a}}{2}\right)^{2}[/tex]
[tex]\begin{aligned}c &=\left(\frac{8}{2}\right)^{2} \\&=\left(\frac{8}{2}\right)^{2} \\c &=4^{2} \\c &=16\end{aligned}[/tex]
Rewriting the expression [tex]x^{2} +8x=0[/tex] and factoring the trinomial, we have,
[tex]\begin{array}{r}{x^{2}+8 x+16=16} \\{(x+4)^{2}=16}\end{array}[/tex]
Taking square root on both sides, we get,
[tex]\begin{aligned}&x+4=\sqrt{16}\\&x+4=\pm 4\end{aligned}[/tex]
Either,
[tex]\begin{array}{r}{x+4=4} \\{x=0}\end{array}[/tex] or [tex]\begin{array}{r}{x+4=-4} \\{x=-8}\end{array}[/tex]
Thus, the value of x is [tex]x=0[/tex] or [tex]x=-8[/tex]
