Solve for x. sqrt((x-5)^(2))=sqrt18

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Recognize Simplification: We start by recognizing that the square root of a square cancels out, so we can simplify sqrt((x-5)^(2)) to |x-5|. This is because the square root and square are inverse operations, but we must consider that the square root function outputs the non-negative root, hence the absolute value. Calculation: sqrt((x-5)^(2)) = |x-5|Set Absolute Value: Next, we set the absolute value of x-5 equal to the square root of 18, which gives us two possible equations: x-5 = sqrt(18) or x-5 = -sqrt(18). This is because the absolute value of a number can be either positive or negative. Calculation: |x-5| = sqrt(18) leads to x-5 = sqrt(18) or x-5 = -sqrt(18)Solve for x (1st Equation): We solve the first equation x-5 = sqrt(18). To find x, we add 5 to both sides of the equation. Calculation: x = sqrt(18) + 5Solve for x (2nd Equation): We solve the second equation x-5 = -sqrt(18). Similarly, we add 5 to both sides of this equation as well. Calculation: x = -sqrt(18) + 5Simplify sqrt(18): Now we simplify sqrt(18). The prime factorization of 18 is 2 * 3^2. We can take the square root of 3^2 out of the square root, which gives us 3. Calculation: sqrt(18) = sqrt(2 * 3^2) = 3 * sqrt(2)Substitute Simplified Form: We substitute the simplified form of sqrt(18) back into the equations for x. Calculation: x = 3 * sqrt(2) + 5 and x = -3 * sqrt(2) + 5Final Solutions: We now have two possible solutions for x, which are x = 3 * sqrt(2) + 5 and x = -3 * sqrt(2) + 5.

Solve for $x$ . $\newline$ $\sqrt{(x-5)^{2}}=\sqrt{18}$

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Solve for xxx.\newline(x−5)2=18 \sqrt{(x-5)^{2}}=\sqrt{18} (x−5)2​=18​

Solve for $x$ . $\newline$ $\sqrt{(x-5)^{2}}=\sqrt{18}$