Find All Complex Solutions square root of 3x-2=-1

$\sqrt{3 x - 2} = - 1$

Step 1

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

${\sqrt{3 x - 2}}^{2} = {(- 1)}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 2}$ as ${(3 x - 2)}^{\frac{1}{2}}$ .

${({(3 x - 2)}^{\frac{1}{2}})}^{2} = {(- 1)}^{2}$

Simplify the left side.

Simplify ${({(3 x - 2)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 2)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 2)}^{\frac{1}{2} \cdot 2} = {(- 1)}^{2}$

Rewrite the expression.

${(3 x - 2)}^{1} = {(- 1)}^{2}$

Simplify.

$3 x - 2 = {(- 1)}^{2}$

Simplify the right side.

Raise $- 1$ to the power of $2$ .

$3 x - 2 = 1$

Step 3

Solve for $x$ .

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

Add $2$ to both sides of the equation.

$3 x = 1 + 2$

Add $1$ and $2$ .

$3 x = 3$

Divide each term in $3 x = 3$ by $3$ and simplify.

Divide each term in $3 x = 3$ by $3$ .

$\frac{3 x}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{3}{3}$

Divide $x$ by $1$ .

$x = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$x = 1$

Step 4

Exclude the solutions that do not make $\sqrt{3 x - 2} = - 1$ true.

$No solution$