Answer
$x = 16$
To check if our solution is correct, we substitute it back into the original equation:
$-3\sqrt {2(16) - 7} + 14 = -1$
Multiply factors within the radical:
$-3\sqrt {32 - 7} + 14 = -1$
Simplify the radical:
$-3\sqrt {25} + 14 = -1$
Evaluate the square root:
$-3(5) + 14 = -1$
Multiply first:
$-15 + 14 = -1$
Add to simplify:
$-1 = -1$
The two sides are equal; therefore, the solution is correct.
Work Step by Step
We want to isolate the radical on the left side of the equation, so first, we subtract $14$ to each side of the equation:
$-3\sqrt {2x - 7} = -15$
Divide both sides by $-3$ to isolate the radical:
$\sqrt {2x - 7} = 5$
Square both sides of the equation:
$2x - 7 = 5^2$
Evaluate the right side of the equation:
$2x - 7 = 25$
Add $7$ to each side of the equation:
$2x = 32$
Divide both sides of the equation by $2$:
$x = 16$
To check if our solution is correct, we substitute it back into the original equation:
$-3\sqrt {2(16) - 7} + 14 = -1$
Multiply factors within the radical:
$-3\sqrt {32 - 7} + 14 = -1$
Simplify the radical:
$-3\sqrt {25} + 14 = -1$
Evaluate the square root:
$-3(5) + 14 = -1$
Multiply first:
$-15 + 14 = -1$
Add to simplify:
$-1 = -1$
The two sides are equal; therefore, the solution is correct.
