Answer
$x = 2.8$
To check to see if our solution is correct, we plug it into the original equation:
$\sqrt[4] {5(2.8) + 2} = 2$
Multiply what is inside the radical sign:
$\sqrt[4] {14 + 2} = 2$
Evaluate what is inside the radical:
$\sqrt[4] {16} = 2$
Take the fourth root:
$2 = 2$
The two sides are equal; therefore, the solution is correct.
Work Step by Step
First, we need to get rid of the radical by raising each side of the equation to the fourth power:
$5x + 2 = 2^4$
Evaluate the right side of the equation:
$5x + 2 = 16$
Subtract $2$ from each side of the equation:
$5x = 14$
Divide both sides of the equation by $5$:
$x = 2.8$
To check to see if our solution is correct, we plug it into the original equation:
$\sqrt[4] {5(2.8) + 2} = 2$
Multiply what is inside the radical sign:
$\sqrt[4] {14 + 2} = 2$
Evaluate what is inside the radical:
$\sqrt[4] {16} = 2$
Take the fourth root:
$2 = 2$
The two sides are equal; therefore, the solution is correct.
