To solve the quadratic equation \(7x^2 = 56x\), we will follow the correct steps to rewrite the equation, factor out the greatest common factor (GCF), set each factor to zero, and find the solutions.
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Put the quadratic in standard form: First, we need to rewrite the equation as follows: \[ 7x^2 - 56x = 0 \]
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Factor out the GCF: The GCF of the terms \(7x^2\) and \(-56x\) is \(7x\), so we factor it out: \[ 7x(x - 8) = 0 \]
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Set each factor equal to zero: \[ 7x = 0 \quad \text{and} \quad x - 8 = 0 \]
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).
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The solutions are: \[ x = 0 \quad \text{and} \quad x = 8 \]
Now, let's compare this with the provided options:
- Option 1 is incorrect.
- Option 2 is correct: The steps are accurately described, leading to the correct solutions of \(x = 0\) and \(x = 8\).
- Option 3 is incorrect: It states that one solution is \(x = -7\), which is wrong.
- Option 4 is incorrect: The equation is incorrectly written as \(7x^2 + 56x = 0\), and it has incorrect solutions.
Thus, the correct response is Option 2.