Solve the equation by the square root property.
\[
(2 x-3)^{2}=23
\]

Answer

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Answer

Final Answer: The solutions to the equation \((2 x-3)^{2}=23\) are \(x = \boxed{3.8979157616563596}\) and \(x = \boxed{-0.8979157616563596}\)

Steps

Step 1 ：Given the equation \((2x - 3)^2 = 23\)

Step 2 ：According to the square root property, if \(x^2 = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\)

Step 3 ：Applying this to our equation, we get two equations: \(2x - 3 = \sqrt{23}\) and \(2x - 3 = -\sqrt{23}\)

Step 4 ：Solving these two equations for x, we get two solutions: \(x = 3.8979157616563596\) and \(x = -0.8979157616563596\)

Step 5 ：Final Answer: The solutions to the equation \((2 x-3)^{2}=23\) are \(x = \boxed{3.8979157616563596}\) and \(x = \boxed{-0.8979157616563596}\)