Question

Solve the equation. $$x^{2}-30=-3$$

Short answer

The roots of the quadratic equation \(x^{2}-30=-3\) are \(x = 3\sqrt{3}\) and \(x = -3\sqrt{3}\).

Step-by-step solution

Move All Terms to One Side of the Equation

First, balance the equation by moving the constant on the right side to the left side, resulting in \(x^{2}-30+3=0\).

Simplify the Equation

Simplify the left side of the equation to get a clearer expression. \(x^{2}-27=0\).

Solve the Simplified Equation for \(x\)

Apply the square root property (\(a^2 = b \Rightarrow a = \sqrt{b}\)) to both sides to solve for \(x\). This gives us two roots: \(x = \sqrt{27}\) and \(x = -\sqrt{27}\). We simplify to get: \(x = 3\sqrt{3}\) and \(x = -3\sqrt{3}\).