To translate the given statement into a quadratic equation, we need to identify the variable in question (let's use \( x \) to represent "the number").
The statement reads: "the product of negative six and a number squared" can be expressed as: \[ -6x^2 \]
Next, "plus the product of five and the same number" translates to: \[ 5x \]
Putting it all together, the equation reads: \[ -6x^2 + 5x = 31 \]
To express this as a standard quadratic equation (set to zero), we can rearrange it as follows: \[ -6x^2 + 5x - 31 = 0 \]
Thus, the quadratic equation equivalent to the given statement is: \[ -6x^2 + 5x - 31 = 0 \]