Answer
$m = -\frac{27}{4}$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {-4(-\frac{27}{4}) - 9} = 6$
Multiply to simplify:
$\sqrt {27 + 9} = 6$
Evaluate what is inside the radical:
$\sqrt {36} = 6$
Evaluate the square root:
$6 = 6$
Work Step by Step
We need to get rid of the radical, so we square both sides of the equation:
$-4m - 9 = 6^{2}$
Evaluate the right side of the equation:
$-4m - 9 = 36$
Add $9$ to both sides of the equation to collect constants on the right side of the equation:
$-4m = 27$
Divide both sides by $-4$ to solve for $m$:
$m = -\frac{27}{4}$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {-4(-\frac{27}{4}) - 9} = 6$
Multiply to simplify:
$\sqrt {27 + 9} = 6$
Evaluate what is inside the radical:
$\sqrt {36} = 6$
Evaluate the square root:
$6 = 6$
