Answer
$x = 258.25$
To check if our solution is correct, we plug it into the original equation:
$\sqrt [5] {4(258.25) - 9} = 4$
Multiply to simplify:
$\sqrt [5] {1033 - 9} = 4$
Evaluate what is inside the radical:
$\sqrt {1024} = 4$
Evaluate the square root:
$4 = 4$
The two sides of the equation are equal; therefore, our solution is correct.
Work Step by Step
We need to get rid of the radical, so we square both sides of the equation:
$4x - 9 = 4^{5}$
Evaluate the right side of the equation:
$4x - 9 = 1024$
Add $9$ to both sides of the equation:
$4x = 1033$
Divide both sides by $4$ to solve for $x$:
$x = 258.25$
To check if our solution is correct, we plug it into the original equation:
$\sqrt [5] {4(258.25) - 9} = 4$
Multiply to simplify:
$\sqrt [5] {1033 - 9} = 4$
Evaluate what is inside the radical:
$\sqrt {1024} = 4$
Evaluate the square root:
$4 = 4$
The two sides of the equation are equal; therefore, our solution is correct.
