Question

solve for ( m ). express your answer as an integer or integers or in simplest radical form. (-5m^2 - 6 = -161)

Explanation:

Step1: Add 6 to both sides

To isolate the term with \( m^2 \), we add 6 to both sides of the equation.

$$ -5m^2 - 6 + 6 = -161 + 6 $$

$$ -5m^2 = -155 $$

Step2: Divide both sides by -5

To solve for \( m^2 \), we divide both sides of the equation by -5.

$$ \frac{-5m^2}{-5} = \frac{-155}{-5} $$

$$ m^2 = 31 $$

Step3: Take square root of both sides

To solve for \( m \), we take the square root of both sides. Remember that when we take the square root of a number, we consider both the positive and negative roots.

$$ m = \pm\sqrt{31} $$

Answer:

\( m = \sqrt{31} \) or \( m = -\sqrt{31} \)