Fowler Peterson
01/17/2024 · High School
Solve using the quadratic formula. \( 6 g^{2}-9=0 \) Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. \( g=\square \) or \( g=\square \)
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Step-by-step Solution
Solve the equation \( 6g^{2}-9=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(6g^{2}-9=0\)
- step1: Add or subtract both sides:
\(6g^{2}=9\)
- step2: Divide both sides:
\(\frac{6g^{2}}{6}=\frac{9}{6}\)
- step3: Divide the numbers:
\(g^{2}=\frac{3}{2}\)
- step4: Simplify the expression:
\(g=\pm \sqrt{\frac{3}{2}}\)
- step5: Simplify the expression:
\(g=\pm \frac{\sqrt{6}}{2}\)
- step6: Separate into possible cases:
\(\begin{align}&g=\frac{\sqrt{6}}{2}\\&g=-\frac{\sqrt{6}}{2}\end{align}\)
- step7: Rewrite:
\(g_{1}=-\frac{\sqrt{6}}{2},g_{2}=\frac{\sqrt{6}}{2}\)
The solutions to the quadratic equation \(6g^{2}-9=0\) using the quadratic formula are:
\[ g_{1}=-\frac{\sqrt{6}}{2}, \quad g_{2}=\frac{\sqrt{6}}{2} \]
or
\[ g_{1}\approx -1.224745, \quad g_{2}\approx 1.224745 \]
Quick Answer
\( g_{1}=-\frac{\sqrt{6}}{2}, g_{2}=\frac{\sqrt{6}}{2} \)
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