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

Ask by Ryan Hilton. in the United States
Jan 23,2025

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The most appropriate strategy for solving the quadratic equation \( g^{2}+18g+50=0 \) is the quadratic formula.

Solución

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.

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Extra Insights

To tackle the equation \( g^{2}+18g+50=0 \), the quadratic formula is your best bet! It’s a lifesaver when dealing with any quadratic equation in the standard form \( ax^2 + bx + c = 0 \). By plugging \( a = 1 \), \( b = 18 \), and \( c = 50 \) into the formula \( g = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), you'll find the roots efficiently, even if they are not nice whole numbers. On the other hand, the zero product property isn't applicable here since the equation is not factored into two binomials. It's great for equations like \( (g + x)(g + y) = 0 \), where you can easily set each factor to zero. With \( g^{2}+18g+50 \), you need to ensure you’re using the right method, and the quadratic formula is the perfect tool for this job!

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