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$Solve for x. Enter the solutions from least to greatest. {:[(x+1)^(2)-36=0],[" lesser "x=◻],[" greater "x=◻]:}$

Solve for $x$ . Enter the solutions from least to greatest. $\newline$ $\begin{array}{l}(x+1)^{2}-36=0 \\ \text { lesser } x=\square \\ \text { greater } x= \square \end{array}$

Full solution

Q. Solve for

x

. Enter the solutions from least to greatest.

\newline

\begin{array}{l}(x+1)^{2}-36=0 \\ \text { lesser } x=\square \\ \text { greater } x= \square \end{array}

Start Equation Isolation: Start with the equation $(x+1)^2 - 36 = 0$ . We need to isolate the squared term. Add $36$ to both sides to move the constant term to the right side of the equation. $(x+1)^2 - 36 + 36 = 0 + 36$
Simplify Perfect Square: Simplify the equation. $\newline$ $(x+1)^2 = 36$ $\newline$ Now we have a perfect square on the left side equal to $36$ .
Take Square Root: Take the square root of both sides to solve for $x + 1$ . $\sqrt{(x+1)^2} = \pm\sqrt{36}$ This gives us two possible solutions for $x + 1$ because the square root of a number can be both positive and negative.
Positive Solution: Solve for the positive square root. $\newline$ $x + 1 = \sqrt{36}$ $\newline$ $x + 1 = 6$ $\newline$ Subtract $1$ from both sides to solve for x. $\newline$ $x = 6 - 1$ $\newline$ $x = 5$ $\newline$ This is the greater solution.
Negative Solution: Solve for the negative square root. $\newline$ $x + 1 = -\sqrt{36}$ $\newline$ $x + 1 = -6$ $\newline$ Subtract $1$ from both sides to solve for $x$ . $\newline$ $x = -6 - 1$ $\newline$ $x = -7$ $\newline$ This is the lesser solution.