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$Solve for x. Enter the solutions from least to greatest. {:[(x-1)^(2)-9=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l} (x-1)^{2}-9=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}$

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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-1)^{2}-9=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Expand the equation: Expand the equation $(x-1)^2 - 9 = 0$ . $\newline$ We need to solve the quadratic equation by first expanding $(x-1)^2$ . $\newline$ $(x-1)^2 = x^2 - 2x + 1$ $\newline$ Now, substitute this back into the original equation: $\newline$ $x^2 - 2x + 1 - 9 = 0$
Simplify the equation: Simplify the equation. $\newline$ Combine like terms to simplify the equation: $\newline$ $x^2 - 2x + 1 - 9 = 0$ $\newline$ $x^2 - 2x - 8 = 0$
Factor the quadratic equation: Factor the quadratic equation. $\newline$ We need to factor $x^2 - 2x - 8$ . $\newline$ $(x - 4)(x + 2) = 0$
Solve for x: Solve for x using the zero product property. $\newline$ Set each factor equal to zero and solve for x: $\newline$ $x - 4 = 0$ or $x + 2 = 0$ $\newline$ $x = 4$ or $x = -2$
Identify the lesser and greater values of x: Identify the lesser and greater values of x. $\newline$ Since $-2$ is less than $4$ , the lesser value of x is $-2$ and the greater value of x is $4$ . $\newline$ lesser $x = -2$ $\newline$ greater $x = 4$

More problems from Evaluate exponential functions

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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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