Question

solve ((y + 2)^2 - 36 = 0), where (y) is a real number. simplify your answer as much as possible. if there is more than one solution, separate them with commas. if there is no solution, click
o solution.\

Explanation:

Step1: Isolate the squared term

Add 36 to both sides of the equation \((y + 2)^2 - 36 = 0\) to get \((y + 2)^2 = 36\).

Step2: Take square roots

Take the square root of both sides. Remember that \(\sqrt{x^2}=\pm x\), so \(y + 2=\pm\sqrt{36}\). Since \(\sqrt{36} = 6\), we have \(y + 2=\pm6\).

Step3: Solve for y (first case)

For the positive case, \(y + 2 = 6\). Subtract 2 from both sides: \(y=6 - 2=4\).

Step4: Solve for y (second case)

For the negative case, \(y + 2=-6\). Subtract 2 from both sides: \(y=-6 - 2=-8\).

Answer:

4, -8