Answer
$x = 24$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {7(24) + 1} = 13$
Multiply to simplify:
$\sqrt {168 + 1} = 13$
Evaluate what is inside the radical:
$\sqrt {169} = 13$
Evaluate the square root:
$13 = 13$
Work Step by Step
We need to get rid of the radical, so we square both sides of the equation:
$7x + 1 = 13^{2}$
Evaluate the right side of the equation:
$7x + 1 = 169$
Subtract $1$ from both sides of the equation to collect constants on the right side of the equation:
$7x = 168$
Divide both sides by $7$ to solve for $x$:
$x = 24$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {7(24) + 1} = 13$
Multiply to simplify:
$\sqrt {168 + 1} = 13$
Evaluate what is inside the radical:
$\sqrt {169} = 13$
Evaluate the square root:
$13 = 13$
