7. \( 3 x^{2}-21=4-x^{2} \)

Solve the equation \( 3x^{2}-21=4-x^{2} \). Solve the quadratic equation by following steps: - step0: Solve using square roots: \(3x^{2}-21=4-x^{2}\) - step1: Add or subtract both sides: \(4x^{2}=25\) - step2: Divide both sides: \(\frac{4x^{2}}{4}=\frac{25}{4}\) - step3: Divide the numbers: \(x^{2}=\frac{25}{4}\) - step4: Simplify the expression: \(x=\pm \sqrt{\frac{25}{4}}\) - step5: Simplify the expression: \(x=\pm \frac{5}{2}\) - step6: Separate into possible cases: \(\begin{align}&x=\frac{5}{2}\\&x=-\frac{5}{2}\end{align}\) - step7: Rewrite: \(x_{1}=-\frac{5}{2},x_{2}=\frac{5}{2}\) The solutions to the equation \(3x^{2}-21=4-x^{2}\) are \(x=-\frac{5}{2}\) and \(x=\frac{5}{2}\), which can also be written as \(x=-2.5\) and \(x=2.5\).