Question
QUESTION \( 9 \cdot 1 \) POINT Solve: \( 9 m^{2}-58 m+24=0 \)
Ask by Reyes Chan. in the United States
Jan 19,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \( m = \frac{4}{9} \) and \( m = 6 \).
Solution
Solve the equation \( 9m^{2}-58m+24=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(9m^{2}-58m+24=0\)
- step1: Factor the expression:
\(\left(m-6\right)\left(9m-4\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&m-6=0\\&9m-4=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&m=6\\&m=\frac{4}{9}\end{align}\)
- step4: Rewrite:
\(m_{1}=\frac{4}{9},m_{2}=6\)
The solutions to the quadratic equation \(9m^{2}-58m+24=0\) are \(m_{1}=\frac{4}{9}\) and \(m_{2}=6\).
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Simplify this solution Mind Expander
To solve the quadratic equation \( 9m^{2}-58m+24=0 \), you can use the quadratic formula, \( m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 9 \), \( b = -58 \), and \( c = 24 \). Calculating the discriminant: \[ b^2 - 4ac = (-58)^2 - 4 \cdot 9 \cdot 24 = 3364 - 864 = 2500 \] Now applying the quadratic formula: \[ m = \frac{58 \pm \sqrt{2500}}{2 \cdot 9} = \frac{58 \pm 50}{18} \] This gives us two possible solutions: 1. \( m = \frac{108}{18} = 6 \) 2. \( m = \frac{8}{18} = \frac{4}{9} \) Thus, the solutions are \( m = 6 \) and \( m = \frac{4}{9} \).
