Question

which values are solutions to the equation $0 = (x - 3)^2 - 1$?
answer
solution #1
solution #2
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Explanation:

Step1: Rearrange the equation

We start with the equation \(0=(x - 3)^2-1\). Add 1 to both sides to get \((x - 3)^2=1\).

Step2: Take square roots

Taking the square root of both sides, we have \(x - 3=\pm\sqrt{1}\), which simplifies to \(x - 3=\pm1\).

Step3: Solve for x (first solution)

For the positive case, \(x - 3 = 1\). Add 3 to both sides: \(x=1 + 3=4\).

Step4: Solve for x (second solution)

For the negative case, \(x - 3=-1\). Add 3 to both sides: \(x=-1 + 3 = 2\).

Answer:

Solution #1: 4
Solution #2: 2