Answer
$x = -4$
Work Step by Step
First, we rewrite this equation so that all terms are on the left side of the equation, and we are left with $0$ on the right side of the equation:
$x^2 + 8x + 16 = 0$
Let's see if we can factor this quadratic polynomial.
To factor a quadratic polynomial equation in the form $ax^2 + bx + c = 0$, we look at factors of the product of $a$ and $c$ such that, when added together, equal $b$.
For the equation $x^2 + 8x + 16 = 0$, $(a)(c)$ is $(1)(16)$, or $16$, but when added together will equal $b$ or $8$. Both factors need to be positive because all terms in the polynomial are positive. We came up with the possibilities:
$(a)(c)$ = $(16)(1)$
$b = 17$
$(a)(c)$ = $(8)(2)$
$b = 10$
$(a)(c)$ = $(4)(4)$
$b = 8$
The third pair, $4$ and $4$, will work. Let us factor the polynomial incorporating these factors:
$(x + 4)(x + 4) = 0$
According to the zero product property, if the product of two factors $a$ and $b$ equals zero, then either $a$ is zero, $b$ is zero, or both equal zero. Since both factors are the same, we only have one solution:
$x + 4 = 0$
Subtract $4$ from each side to solve for $x$:
$x = -4$
The solution is $x = 3, -1$.
