Of the strategies listed, which is most appropriate for solving \( g^{2}+18 g+50=0 \) ? square root property quadratic formula zero product property

To solve the quadratic equation \( g^{2}+18g+50=0 \), we can use the quadratic formula. The quadratic formula is given by: \[ g = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} \] In this case, \( a = 1 \), \( b = 18 \), and \( c = 50 \). Substitute these values into the quadratic formula to find the solutions for \( g \). Solve the quadratic equation by following steps: - step0: Solve using the quadratic formula: \(g^{2}+18g+50=0\) - step1: Solve using the quadratic formula: \(g=\frac{-18\pm \sqrt{18^{2}-4\times 50}}{2}\) - step2: Simplify the expression: \(g=\frac{-18\pm \sqrt{124}}{2}\) - step3: Simplify the expression: \(g=\frac{-18\pm 2\sqrt{31}}{2}\) - step4: Separate into possible cases: \(\begin{align}&g=\frac{-18+2\sqrt{31}}{2}\\&g=\frac{-18-2\sqrt{31}}{2}\end{align}\) - step5: Simplify the expression: \(\begin{align}&g=-9+\sqrt{31}\\&g=\frac{-18-2\sqrt{31}}{2}\end{align}\) - step6: Simplify the expression: \(\begin{align}&g=-9+\sqrt{31}\\&g=-9-\sqrt{31}\end{align}\) - step7: Rewrite: \(g_{1}=-9-\sqrt{31},g_{2}=-9+\sqrt{31}\) The solutions to the quadratic equation \( g^{2}+18g+50=0 \) are \( g_{1}=-9-\sqrt{31} \) and \( g_{2}=-9+\sqrt{31} \). Therefore, the most appropriate strategy for solving the quadratic equation \( g^{2}+18g+50=0 \) is the quadratic formula.