Solve for x (2x+1)^(1/2)+4=13

${(2 x + 1)}^{\frac{1}{2}} + 4 = 13$

Step 1

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

Subtract $4$ from both sides of the equation.

${(2 x + 1)}^{\frac{1}{2}} = 13 - 4$

Subtract $4$ from $13$ .

${(2 x + 1)}^{\frac{1}{2}} = 9$

Step 2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${({(2 x + 1)}^{\frac{1}{2}})}^{2} = 9^{2}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${({(2 x + 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x + 1)}^{\frac{1}{2}})}^{2}$ .

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

${(2 x + 1)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x + 1)}^{\frac{1}{2} \cdot 2} = 9^{2}$

Rewrite the expression.

${(2 x + 1)}^{1} = 9^{2}$

Simplify.

$2 x + 1 = 9^{2}$

Simplify the right side.

Raise $9$ to the power of $2$ .

$2 x + 1 = 81$

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.

$2 x = 81 - 1$

Subtract $1$ from $81$ .

$2 x = 80$

Divide each term in $2 x = 80$ by $2$ and simplify.

Divide each term in $2 x = 80$ by $2$ .

$\frac{2 x}{2} = \frac{80}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{80}{2}$

Divide $x$ by $1$ .

$x = \frac{80}{2}$

Simplify the right side.

Divide $80$ by $2$ .

$x = 40$

Solve for x (2x+1)^(1/2)+4=13

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