Find both solutions to the equation. 100+(n-2)^(2)=116

Isolate squared term: Start by isolating the squared term on one side of the equation. Subtract 100 from both sides of the equation to get: 100 + (n - 2)^2 - 100 = 116 - 100 This simplifies to: (n - 2)^2 = 16Take square root: Take the square root of both sides of the equation to solve for n - 2. √((n - 2)^2) = ±√16 This gives us two possible solutions because the square root of a number can be both positive and negative: n - 2 = ±4Solve for n: Solve for n by adding 2 to both sides of each equation. For the positive root: n - 2 + 2 = 4 + 2 n = 6 For the negative root: n - 2 + 2 = -4 + 2 n = -2

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Find both solutions to the equation.
100+(n-2)^(2)=116

Find both solutions to the equation. $\newline$ $100+(n-2)^{2}=116$

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Algebra 2

Simplify rational expressions

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Q. Find both solutions to the equation.

\newline

100+(n-2)^{2}=116

Isolate squared term: Start by isolating the squared term on one side of the equation. $\newline$ Subtract $100$ from both sides of the equation to get: $\newline$ $100 + (n - 2)^2 - 100 = 116 - 100$ $\newline$ This simplifies to: $\newline$ $(n - 2)^2 = 16$
Take square root: Take the square root of both sides of the equation to solve for $n - 2$ . $\sqrt{(n - 2)^2} = \pm\sqrt{16}$ This gives us two possible solutions because the square root of a number can be both positive and negative: $n - 2 = \pm4$
Solve for n: Solve for n by adding $2$ to both sides of each equation. $\newline$ For the positive root: $\newline$ $n - 2 + 2 = 4 + 2$ $\newline$ $n = 6$ $\newline$ For the negative root: $\newline$ $n - 2 + 2 = -4 + 2$ $\newline$ $n = -2$