Problem

Solve the quadratic equation by using the square root property. (Enter your answers as a comma-separated list.) \[ (x-3)^{2}=7 \] \[ x= \]

Solution

Step 1 :The square root property states that if \(x^2 = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\). In this case, we have \((x-3)^2 = 7\), so \(x-3 = \sqrt{7}\) or \(x-3 = -\sqrt{7}\).

Step 2 :Solving for \(x\) in both cases will give us the solutions to the equation.

Step 3 :The solutions to the equation \((x-3)^{2}=7\) are \(x = 3 + \sqrt{7}\) and \(x = 3 - \sqrt{7}\).

Step 4 :In decimal form, these are approximately \(x = 5.65\) and \(x = 0.35\).

Step 5 :Final Answer: Therefore, the solutions are \(\boxed{5.65, 0.35}\).

From Solvely APP
Source: https://solvelyapp.com/problems/7535/

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