Question

solve the following quadratic equation.
$(x - 3)^2 = 4$
enter multiple answers separated by a comma or enter none if there are no real solutions.

Explanation:

Step1: Take square root of both sides

Take the square root of each side of the equation \((x - 3)^2=4\). We know that if \(y^{2}=a\) (\(a\geq0\)), then \(y = \pm\sqrt{a}\). So, applying this property, we get \(x - 3=\pm\sqrt{4}\)

Step2: Simplify the square root

Simplify \(\sqrt{4}\), we know that \(\sqrt{4} = 2\). So the equation becomes \(x-3=\pm2\)

Step3: Solve for x in two cases

Case 1: When we take the positive sign

If \(x - 3=2\), then add 3 to both sides of the equation. \(x=2 + 3=5\)

Case 2: When we take the negative sign

If \(x - 3=- 2\), then add 3 to both sides of the equation. \(x=-2 + 3 = 1\)

Answer:

1,5