Answer
$x = \frac{221}{3}$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {3(\frac{221}{3}) + 4} = 15$
Evaluate the fraction first:
$\sqrt {221 + 4} = 15$
Evaluate what is inside the radical:
$\sqrt {225} = 15$
Evaluate the square root:
$15 = 15$
Work Step by Step
We need to get rid of the radical, so we square both sides of the equation:
$3x + 4 = 15^{2}$
Evaluate the right side of the equation:
$3x + 4 = 225$
Subtract $4$ from both sides of the equation to collect constants on the right side of the equation:
$3x = 221$
Divide both sides by $3$ to solve for $x$:
$x = \frac{221}{3}$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {3(\frac{221}{3}) + 4} = 15$
Evaluate the fraction first:
$\sqrt {221 + 4} = 15$
Evaluate what is inside the radical:
$\sqrt {225} = 15$
Evaluate the square root:
$15 = 15$
