Young Savage
06/01/2023 · Middle School
Solve using the quadratic formula. \( 6 u^{2}-8 u+2=0 \) Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. \( u=\square \) or \( u=\square \) Submit
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Step-by-step Solution
Solve the equation \( 6u^{2}-8u+2=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(6u^{2}-8u+2=0\)
- step1: Factor the expression:
\(2\left(u-1\right)\left(3u-1\right)=0\)
- step2: Divide the terms:
\(\left(u-1\right)\left(3u-1\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&u-1=0\\&3u-1=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&u=1\\&u=\frac{1}{3}\end{align}\)
- step5: Rewrite:
\(u_{1}=\frac{1}{3},u_{2}=1\)
The solutions to the quadratic equation \(6u^{2}-8u+2=0\) using the quadratic formula are \(u=\frac{1}{3}\) or \(u=1\).
Quick Answer
\( u=\frac{1}{3} \) or \( u=1 \)
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