Solve the following quadratic equation using square roots: (x+3)2=36

Question

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Answer 1

To solve the quadratic equation \((x + 3)^2 = 36\) using square roots, follow these steps:

1. Take the square root of both sides: \[ x + 3 = \pm \sqrt{36} \]

2. Calculate the square root: \[ x + 3 = \pm 6 \]

3. Solve for \(x\) for both cases:

   • Case 1: \[ x + 3 = 6 \] Subtract 3 from both sides: \[ x = 6 - 3 = 3 \]

   • Case 2: \[ x + 3 = -6 \] Subtract 3 from both sides: \[ x = -6 - 3 = -9 \]

4. The solutions are: \[ x = 3 \quad \text{and} \quad x = -9 \]

Thus, the final solutions to the equation \((x + 3)^2 = 36\) are \(x = 3\) and \(x = -9\).