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

Taking the square root of both sides of the equation \((x - 3)^2 = 4\), we get \(x - 3=\pm\sqrt{4}\). Since \(\sqrt{4} = 2\), this simplifies to \(x - 3=\pm2\).

Step2: Solve for x in two cases

• Case 1: When \(x - 3 = 2\), add 3 to both sides. So \(x=2 + 3=5\).
• Case 2: When \(x - 3=- 2\), add 3 to both sides. So \(x=-2 + 3 = 1\).

Answer:

\(1,5\)