Question

solve the quadratic equation by the square root method and write the solutions in radical form. simplify the solutions.
(8x + 8)^2 = 27
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Explanation:

Step1: Take square roots of both sides

$$8x + 8 = \pm\sqrt{27}$$

Step2: Simplify the radical term

$$\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$$
So, $8x + 8 = \pm3\sqrt{3}$

Step3: Isolate the variable term

$$8x = -8 \pm 3\sqrt{3}$$

Step4: Solve for $x$

$$x = \frac{-8 \pm 3\sqrt{3}}{8} = -1 \pm \frac{3\sqrt{3}}{8}$$

Answer:

$x = -1 + \frac{3\sqrt{3}}{8}$ or $x = -1 - \frac{3\sqrt{3}}{8}$