Answer
$x = 23$
Work Step by Step
Rewrite exponents as radicals:
$\sqrt {2x + 3} - 7 = 0$
Isolate the radical:
$\sqrt {2x + 3} = 7$
Square both sides of the equation to eliminate the radical:
$2x + 3 = 49$
$2x = 46$
Divide both sides of the equation by $2$:
$x = 23$
To check if we have an extraneous solution, we substitute the solution into the original equation to see if the two sides equal one another.
$\sqrt {2(23) + 3} - 7 = 0$
Simplify the radicand:
$\sqrt {49} - 7 = 0$
Take the square root:
$7 - 7 = 0$
Combine like terms:
$0 = 0$
Both sides are equal; therefore, this solution is valid.
