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$Solve for x. {:[x^(2)+16 x+64=0],[x=◻]:}$

Solve for $x$ . $\newline$ $\begin{array}{l} x^{2}+16 x+64=0 \\ x=\square \end{array}$

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Solve a quadratic equation by factoring

Full solution

Q. Solve for

x

.

\newline

\begin{array}{l} x^{2}+16 x+64=0 \\ x=\square \end{array}

Identify the quadratic equation: Identify the quadratic equation to solve. $\newline$ We have the quadratic equation $x^2 + 16x + 64 = 0$ .
Find the numbers that satisfy the conditions: Look for two numbers that multiply to $64$ and add up to $16$ . $\newline$ The numbers $8$ and $8$ satisfy both conditions because $8 \times 8 = 64$ and $8 + 8 = 16$ .
Write the equation in factored form: Write the equation in factored form. $\newline$ Since the numbers we found are both $8$ , we can write the equation as $(x + 8)(x + 8) = 0$ .
Set each factor equal to zero and solve for $x$ : Set each factor equal to zero and solve for $x$ . $\newline$ First, set the first factor equal to zero: $x +$ $8$ = $0$ . $\newline$ Subtract $8$ from both sides to solve for $x$ : $x =$ $-8$ .
Determine the solution for $x$ : Since both factors are the same, the second factor $(x +$ $8$ ) also equals zero and gives the same solution for $x$ . $\newline$ Therefore, $x =$ $-8$ is the only solution.

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