Solve by Factoring fourth root of 4x+1-2=0

$\sqrt[4]{4 x + 1} - 2 = 0$

Step 1

Add $2$ to both sides of the equation.

$\sqrt[4]{4 x + 1} = 2$

Step 2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{4 x + 1}}^{4} = 2^{4}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{4 x + 1}$ as ${(4 x + 1)}^{\frac{1}{4}}$ .

${({(4 x + 1)}^{\frac{1}{4}})}^{4} = 2^{4}$

Simplify the left side.

Simplify ${({(4 x + 1)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(4 x + 1)}^{\frac{1}{4}})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(4 x + 1)}^{\frac{1}{4} \cdot 4} = 2^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(4 x + 1)}^{\frac{1}{4} \cdot 4} = 2^{4}$

Rewrite the expression.

${(4 x + 1)}^{1} = 2^{4}$

Simplify.

$4 x + 1 = 2^{4}$

Simplify the right side.

Raise $2$ to the power of $4$ .

$4 x + 1 = 16$

Step 4

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$4 x = 16 - 1$

Subtract $1$ from $16$ .

$4 x = 15$

Divide each term in $4 x = 15$ by $4$ and simplify.

Divide each term in $4 x = 15$ by $4$ .

$\frac{4 x}{4} = \frac{15}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{15}{4}$

Divide $x$ by $1$ .

$x = \frac{15}{4}$