Use a graphing utility to solve the equation In \( x=x^{2}-3 \) The solution set is \( \} \) (Use a comma to separate answers as needed Round to two decimal places as needed)

Solve the equation \( x=x^{2}-3 \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(x=x^{2}-3\) - step1: Swap the sides: \(x^{2}-3=x\) - step2: Move the expression to the left side: \(x^{2}-3-x=0\) - step3: Rewrite in standard form: \(x^{2}-x-3=0\) - step4: Solve using the quadratic formula: \(x=\frac{1\pm \sqrt{\left(-1\right)^{2}-4\left(-3\right)}}{2}\) - step5: Simplify the expression: \(x=\frac{1\pm \sqrt{13}}{2}\) - step6: Separate into possible cases: \(\begin{align}&x=\frac{1+\sqrt{13}}{2}\\&x=\frac{1-\sqrt{13}}{2}\end{align}\) - step7: Rewrite: \(x_{1}=\frac{1-\sqrt{13}}{2},x_{2}=\frac{1+\sqrt{13}}{2}\) The solutions to the equation \(x = x^2 - 3\) are \(x \approx -1.302776\) and \(x \approx 2.302776\).