To solve the quadratic equation \( 7x^2 = 56x \), we first need to rearrange it into standard form.
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Put the equation in standard form: \[ 7x^2 - 56x = 0 \]
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Now, factor out the GCF (Greatest Common Factor): \[ 7x(x - 8) = 0 \]
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Set each factor equal to zero:
- First factor: \( 7x = 0 \) → \( x = 0 \)
- Second factor: \( x - 8 = 0 \) → \( x = 8 \)
The solutions to the equation are:
- \( x = 0 \)
- \( x = 8 \)
Looking at the responses you provided, the correct table is:
Response:
Put the quadratic in standard form \(7x^2 - 56x = 0\)
Factor out the GCF \(7x(x - 8) = 0\)
Set each factor equal to zero \(7x = 0\) and \(x - 8 = 0\)
The solutions are \(x = 0\) and \(x = 8\).
This response clearly outlines the steps correctly and provides the accurate solutions.