Solve the Rational Equation for x square root of 7x-1=-2

$\sqrt{7 x - 1} = - 2$

Step 1

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

${\sqrt{7 x - 1}}^{2} = {(- 2)}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x - 1}$ as ${(7 x - 1)}^{\frac{1}{2}}$ .

${({(7 x - 1)}^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Simplify the left side.

Simplify ${({(7 x - 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(7 x - 1)}^{\frac{1}{2}})}^{2}$ .

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

${(7 x - 1)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 x - 1)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Rewrite the expression.

${(7 x - 1)}^{1} = {(- 2)}^{2}$

Simplify.

$7 x - 1 = {(- 2)}^{2}$

Simplify the right side.

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

$7 x - 1 = 4$

Step 3

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$7 x = 4 + 1$

Add $4$ and $1$ .

$7 x = 5$

Divide each term in $7 x = 5$ by $7$ and simplify.

Divide each term in $7 x = 5$ by $7$ .

$\frac{7 x}{7} = \frac{5}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{5}{7}$

Divide $x$ by $1$ .

$x = \frac{5}{7}$

Step 4

Exclude the solutions that do not make $\sqrt{7 x - 1} = - 2$ true.

$No solution$