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, we start by taking the square root of both sides:

\[ x + 3 = \pm 6 \]

This gives us two equations to solve:

1. \(x + 3 = 6\)
2. \(x + 3 = -6\)

Now we solve each equation individually.

For the first equation: \[ x + 3 = 6 \] Subtract 3 from both sides: \[ x = 6 - 3 \] \[ x = 3 \]

For the second equation: \[ x + 3 = -6 \] Subtract 3 from both sides: \[ x = -6 - 3 \] \[ x = -9 \]

Thus, the solutions to the equation \((x + 3)^2 = 36\) are: \[ x = 3 \quad \text{and} \quad x = -9 \]