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$Solve for x. Enter the solutions from least to greatest. {:[(x+5)^(2)-64=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} (x+5)^{2}-64=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

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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+5)^{2}-64=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 $(x+5)^2 - 64 = 0$ , which is a quadratic equation in the form of a perfect square difference.
Factor using Difference of Squares: Factor the equation using the difference of squares formula, $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ $(x+5)^2 - 64$ can be factored as $((x+5) + 8)((x+5) - 8)$ because $64$ is $8^2$ . $\newline$ So, the factored form is $(x+5+8)(x+5-8)$ which simplifies to $(x+13)(x-3)$ .
Set and Solve for x: Set each factor equal to zero and solve for x. $\newline$ First, set $x+13$ equal to zero: $x+13 = 0$ , which gives $x = -13$ . $\newline$ Second, set $x-3$ equal to zero: $x-3 = 0$ , which gives $x = 3$ .
Identify Lesser and Greater Solutions: Identify the lesser and greater solutions. $\newline$ The lesser solution is $x = -13$ , and the greater solution is $x = 3$ .

More problems from Evaluate exponential functions

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x

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g(t) = 3^t

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f(x) = 6x

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f(x) = 6^x

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f(x) = \frac{1}{6^x}

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f(x) = \frac{x}{6}

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