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$Solve for x. Enter the solutions from least to greatest. {:[(x+7)^(2)-49=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} (x+7)^{2}-49=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

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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+7)^{2}-49=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Identify equation to solve: Identify the equation to solve for $x$ . $(x+7)^2 - 49 = 0$
Recognize difference of squares: Recognize that the equation is a difference of squares, which can be factored. $(x+7)^2 - 49 = (x+7 + 7)(x+7 - 7)$
Simplify factored form: Simplify the factored form. $(x+7 + 7)(x+7 - 7) = (x+14)(x)$
Set factors equal to zero: Set each factor equal to zero to find the solutions for $x$ . $x + 14 = 0$ or $x = 0$
Solve for x: Solve for x in each equation. $\newline$ $x + 14 = 0 \rightarrow x = -14$ $\newline$ $x = 0 \rightarrow x = 0$
Identify lesser and greater values of x: Identify the lesser and greater values of x. $\newline$ lesser x = $-14$ $\newline$ greater x = $0$

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