To find the quadratic equation equivalent to the given statement, we will break down the phrase step by step.
The statement is: "the product of negative six and a number squared, plus the product of five and the same number is thirty-one."
Let's denote the number as \(x\).
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"The product of negative six and a number squared" is: \[-6x^2\]
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"The product of five and the same number" is: \[5x\]
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Putting it all together with the phrase "is thirty-one": \[-6x^2 + 5x = 31\]
Now we can see that the equivalent quadratic equation is: \[-6x^2 + 5x = 31\]
So the correct answer is: \[-6x² + 5x = 31\]