To factor out the greatest common factor (GCF) and solve the quadratic equation \(7x^2 = 56x\), we can follow these steps:
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Set the equation to zero: We want all terms on one side of the equation. \[ 7x^2 - 56x = 0 \]
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Factor the left-hand side: Identify the GCF of the terms.
- The GCF of \(7x^2\) and \(56x\) is \(7x\).
- Factor out \(7x\): \[ 7x(x - 8) = 0 \]
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Use the Zero Product Property: Set each factor equal to zero.
- \(7x = 0\) or \(x - 8 = 0\)
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Solve each equation:
- From \(7x = 0\): \[ x = 0 \]
- From \(x - 8 = 0\): \[ x = 8 \]
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Write down the final solution: The solutions to the equation \(7x^2 = 56x\) are: \[ x = 0 \quad \text{or} \quad x = 8 \]
In summary, to solve the quadratic equation \(7x^2 = 56x\), we factor out the GCF \(7x\), set each factor to zero, and solve to find the solutions \(x = 0\) and \(x = 8\).