Pregunta
100 points possible Answered: 1122 Question 2 Solve by the quadratic formula: \[ 3 x^{2}-10 x-8=0 \] List your answers separated by commas, for example: \( \frac{2}{3}, \frac{5}{2} \) type \( 2 / 3,5 / 2^{\prime \prime} \) or \( \frac{5 \pm 2 \sqrt{3}}{5} \), type \( (5+-2 \) sqrt \( (3)) / 5^{\prime \prime} \). \( \left(5+-2\right. \) sqrt(3)) \( / 5^{\prime \prime} \). \( \square \) Next Question
Ask by Martin Mccoy. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( x = -\frac{2}{3}, 4 \)
Solución
Solve the equation \( 3x^2-10x-8=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(3x^{2}-10x-8=0\)
- step1: Factor the expression:
\(\left(x-4\right)\left(3x+2\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-4=0\\&3x+2=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=4\\&x=-\frac{2}{3}\end{align}\)
- step4: Rewrite:
\(x_{1}=-\frac{2}{3},x_{2}=4\)
The solutions to the quadratic equation \(3x^2-10x-8=0\) are \(x_{1}=-\frac{2}{3}\) and \(x_{2}=4\).
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Como
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The Deep Dive
To solve the quadratic equation \(3x^2 - 10x - 8 = 0\) using the quadratic formula, where \(a = 3\), \(b = -10\), and \(c = -8\), we apply the formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Calculating the discriminant: \[ b^2 - 4ac = (-10)^2 - 4(3)(-8) = 100 + 96 = 196 \] Now plug in the values: \[ x = \frac{10 \pm \sqrt{196}}{6} = \frac{10 \pm 14}{6} \] Calculating the two possible solutions: 1. \(x_1 = \frac{24}{6} = 4\) 2. \(x_2 = \frac{-4}{6} = -\frac{2}{3}\) Thus, the two solutions are: 4, -2/3

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