Answer
$x = 59$
To check if our solution is correct, we plug it into the original equation:
$2\sqrt {59 + 5} - 12 = 4$
Evaluate what is inside the radical:
$2\sqrt {64} - 12 = 4$
Evaluate the radical:
$2(8) - 12 = 4$
Multiply to simplify:
$16 - 12 = 4$
Add to simplify:
$4 = 4$
Work Step by Step
We need to isolate the radical, so we add $12$ to each side of the equation first:
$2\sqrt {x + 5} = 16$
Divide both sides by $2$ to isolate the radical:
$\sqrt {x + 5} = 8$
We need to get rid of the radical, so we square both sides of the equation:
$x + 5 = 8^{2}$
Evaluate the right side of the equation:
$x + 5 = 64$
Subtract $5$ from both sides of the equation to solve for x:
$x = 59$
To check if our solution is correct, we plug it into the original equation:
$2\sqrt {59 + 5} - 12 = 4$
Evaluate what is inside the radical:
$2\sqrt {64} - 12 = 4$
Evaluate the radical:
$2(8) - 12 = 4$
Multiply to simplify:
$16 - 12 = 4$
Add to simplify:
$4 = 4$
