Question 5 Solve for the roots in simplest form using the quadratic formula: \[ x^{2}+97=20 x \] Answer คAdditional Solution \( \Theta \) No Solution

Solve the equation \( x^{2}+97=20x \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x^{2}+97=20x\) - step1: Move the expression to the left side: \(x^{2}+97-20x=0\) - step2: Rewrite in standard form: \(x^{2}-20x+97=0\) - step3: Solve using the quadratic formula: \(x=\frac{20\pm \sqrt{\left(-20\right)^{2}-4\times 97}}{2}\) - step4: Simplify the expression: \(x=\frac{20\pm \sqrt{12}}{2}\) - step5: Simplify the expression: \(x=\frac{20\pm 2\sqrt{3}}{2}\) - step6: Separate into possible cases: \(\begin{align}&x=\frac{20+2\sqrt{3}}{2}\\&x=\frac{20-2\sqrt{3}}{2}\end{align}\) - step7: Simplify the expression: \(\begin{align}&x=10+\sqrt{3}\\&x=\frac{20-2\sqrt{3}}{2}\end{align}\) - step8: Simplify the expression: \(\begin{align}&x=10+\sqrt{3}\\&x=10-\sqrt{3}\end{align}\) - step9: Rewrite: \(x_{1}=10-\sqrt{3},x_{2}=10+\sqrt{3}\) The roots of the equation \(x^{2}+97=20x\) using the quadratic formula are \(x_{1}=10-\sqrt{3}\) and \(x_{2}=10+\sqrt{3}\).