Solve the Rational Equation for x square root of 5x+1-6=0

$\sqrt{5 x + 1} - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$\sqrt{5 x + 1} = 6$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{5 x + 1}}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x + 1}$ as ${(5 x + 1)}^{\frac{1}{2}}$ .

${({(5 x + 1)}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(5 x + 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 x + 1)}^{\frac{1}{2}})}^{2}$ .

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

${(5 x + 1)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x + 1)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(5 x + 1)}^{1} = 6^{2}$

Simplify.

$5 x + 1 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$5 x + 1 = 36$

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.

$5 x = 36 - 1$

Subtract $1$ from $36$ .

$5 x = 35$

Divide each term in $5 x = 35$ by $5$ and simplify.

Divide each term in $5 x = 35$ by $5$ .

$\frac{5 x}{5} = \frac{35}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{35}{5}$

Divide $x$ by $1$ .

$x = \frac{35}{5}$

Simplify the right side.

Divide $35$ by $5$ .

$x = 7$