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$Solve for x. Enter the solutions from least to greatest. {:[(x+6)^(2)-16=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} (x+6)^{2}-16=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

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Evaluate exponential functions

Full solution

Q. Solve for

x

. Enter the solutions from least to greatest.

\newline

\begin{array}{l} (x+6)^{2}-16=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Write and Identify Equation: Write down the given equation and identify the type of equation. $\newline$ The given equation is $(x+6)^2 - 16 = 0$ . This is a quadratic equation in the form of a perfect square trinomial minus a constant.
Factor using Difference of Squares: Factor the equation using the difference of squares formula. $\newline$ The equation $(x+6)^2 - 16 = 0$ can be factored as $((x+6) + 4)((x+6) - 4) = 0$ , because $16$ is a perfect square and can be written as $4^2$ .
Set Factors Equal and Solve: Set each factor equal to zero and solve for $x$ .
$(x+6) + 4 = 0$ or $(x+6) - 4 = 0$
This gives us two separate equations to solve:
$1$ . $x + 6 + 4 = 0$
$2$ . $x + 6 - 4 = 0$
Solve First Equation: Solve the first equation for $x$ . $x + 10 = 0$ Subtract $10$ from both sides: $x = -10$
Solve Second Equation: Solve the second equation for $x$ . $x + 2 = 0$ Subtract $2$ from both sides: $x = -2$
Identify Lesser and Greater Solutions: Identify the lesser and greater solutions. $\newline$ The lesser value of $x$ is $-10$ , and the greater value of $x$ is $-2$ .

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