Question

question

solve: \\(5m^2 - m - 6 = 0\\). multiple answers, if any, s

provide your answer below:

\\(m = \\)

Explanation:

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<reasoning>

Identify the quadratic equation

We need to solve the quadratic equation:
\[5m^2 - m - 6 = 0\]

Factor the quadratic expression

Using the AC Method and Factoring by Grouping knowledge points
\[

$$\begin{aligned} &a \cdot c = 5 \cdot (-6) = -30\\ &-6 + 5 = -1\\ &5m^2 - 6m + 5m - 6 = 0\\ &m(5m - 6) + 1(5m - 6) = 0\\ &(5m - 6)(m + 1) = 0 \end{aligned}$$

\]

Solve for the variable

Using the Zero Product Property and Solving Linear Equations knowledge points
\[

$$\begin{aligned} &5m - 6 = 0 \implies m = \frac{6}{5}\\ &m + 1 = 0 \implies m = -1 \end{aligned}$$

\]
</reasoning>

<answer>
Solve: \(5m^2 - m - 6 = 0\). Multiple answers, if any, should be separated by a comma.

Provide your answer below:

\(m =\) <blank>\(\frac{6}{5}, -1\)</blank>
</answer>

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Answer:

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<reasoning>

Identify the quadratic equation

We need to solve the quadratic equation:
\[5m^2 - m - 6 = 0\]

Factor the quadratic expression

Using the AC Method and Factoring by Grouping knowledge points
\[

$$\begin{aligned} &a \cdot c = 5 \cdot (-6) = -30\\ &-6 + 5 = -1\\ &5m^2 - 6m + 5m - 6 = 0\\ &m(5m - 6) + 1(5m - 6) = 0\\ &(5m - 6)(m + 1) = 0 \end{aligned}$$

\]

Solve for the variable

Using the Zero Product Property and Solving Linear Equations knowledge points
\[

$$\begin{aligned} &5m - 6 = 0 \implies m = \frac{6}{5}\\ &m + 1 = 0 \implies m = -1 \end{aligned}$$

\]
</reasoning>

<answer>
Solve: \(5m^2 - m - 6 = 0\). Multiple answers, if any, should be separated by a comma.

Provide your answer below:

\(m =\) <blank>\(\frac{6}{5}, -1\)</blank>
</answer>

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"knowledge_point": [
"Mathematics",
"Algebra",
"Solving Quadratic Equations by Factoring"
]
}
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