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Select the quadratic equation that is equivalent to: The product of 4 and a number squared, minus the product of 8 and that same number is 7

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Let's translate the statement step by step into a quadratic equation.

  1. "The product of 4 and a number squared" can be expressed as: \[ 4x^2 \] where \( x \) is the number.

  2. "The product of 8 and that same number" can be expressed as: \[ 8x \]

  3. Putting it all together, we have: \[ 4x^2 - 8x = 7 \]

  4. To transform this into standard form, we can move 7 to the left side of the equation: \[ 4x^2 - 8x - 7 = 0 \]

Therefore, the equivalent quadratic equation is: \[ 4x^2 - 8x - 7 = 0 \]