Solve by Factoring square root of 2x+1=-3

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

Step 1

Add $3$ to both sides of the equation.

$\sqrt{2 x + 1} + 3 = 0$

Step 2

Subtract $3$ from both sides of the equation.

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

Step 3

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

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

Step 4

Simplify each side of the equation.

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 3$ to the power of $2$ .

$2 x + 1 = 9$

Step 5

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$2 x = 9 - 1$

Subtract $1$ from $9$ .

$2 x = 8$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$

Step 6

Exclude the solutions that do not make $\sqrt{2 x + 1} + 3 = 0$ true.

$No solution$

Solve by Factoring square root of 2x+1=-3

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