Question

Select the quadratic equation that is equivalent to the product of negative six and a number squared, plus the product of five and the same number is thirty-one. (1 point) - 6x ^ 2 + 5x = 31; 6x ^ 2 - 5x = 31; - 6x ^ 2 - 5x + 31; - 6x ^ 2 + 5x + 31

Answer 1

To form the quadratic equation from the given statement, let's break it down 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 the variable \( x \) represent "the number."

1. **Product of negative six and a number squared**: This translates to \( -6x^2 \).
2. **Product of five and the same number**: This translates to \( 5x \).
3. **The equation states this total is equal to thirty-one**: So we have:
\[
-6x^2 + 5x = 31
\]

Now, rearranging this equation to standard form:
\[
-6x^2 + 5x - 31 = 0
\]

However, this is not one of the options provided. But the equivalent expression in terms of equality to \( 31 \) would be \( -6x^2 + 5x - 31 = 0 \).

The closest form among the given choices that reflects this equation accurately is:

**-6x² + 5x = 31**.

Hence, the equivalent quadratic equation is:
**-6x² + 5x = 31**.