Solve for x square root of (5x+10)^2=-1

$\sqrt{{(5 x + 10)}^{2}} = - 1$

Step 1

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

${\sqrt{{(5 x + 10)}^{2}}}^{2} = {(- 1)}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{{(5 x + 10)}^{2}}$ as ${(5 x + 10)}^{\frac{2}{2}}$ .

${({(5 x + 10)}^{\frac{2}{2}})}^{2} = {(- 1)}^{2}$

Divide $2$ by $2$ .

${({(5 x + 10)}^{1})}^{2} = {(- 1)}^{2}$

Simplify the left side.

Multiply the exponents in ${({(5 x + 10)}^{1})}^{2}$ .

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

${(5 x + 10)}^{1 \cdot 2} = {(- 1)}^{2}$

Multiply $2$ by $1$ .

${(5 x + 10)}^{2} = {(- 1)}^{2}$

Simplify the right side.

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

${(5 x + 10)}^{2} = 1$

Step 3

Solve for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$5 x + 10 = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$5 x + 10 = \pm 1$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$5 x + 10 = 1$

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

Subtract $10$ from both sides of the equation.

$5 x = 1 - 10$

Subtract $10$ from $1$ .

$5 x = - 9$

Divide each term in $5 x = - 9$ by $5$ and simplify.

Divide each term in $5 x = - 9$ by $5$ .

$\frac{5 x}{5} = \frac{- 9}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 9}{5}$

Divide $x$ by $1$ .

$x = \frac{- 9}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{9}{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$5 x + 10 = - 1$

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

Subtract $10$ from both sides of the equation.

$5 x = - 1 - 10$

Subtract $10$ from $- 1$ .

$5 x = - 11$

Divide each term in $5 x = - 11$ by $5$ and simplify.

Divide each term in $5 x = - 11$ by $5$ .

$\frac{5 x}{5} = \frac{- 11}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 11}{5}$

Divide $x$ by $1$ .

$x = \frac{- 11}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{11}{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = - \frac{9}{5}, - \frac{11}{5}$

Step 4

Exclude the solutions that do not make $\sqrt{{(5 x + 10)}^{2}} = - 1$ true.

$No solution$

Solve for x square root of (5x+10)^2=-1

Related Questions

Support LCMGCF.com by disabling your adblocker.