Solve for v -3 = square root of -3-v-4

$- 3 = \sqrt{- 3 - v} - 4$

Step 1

Rewrite the equation as $\sqrt{- 3 - v} - 4 = - 3$ .

$\sqrt{- 3 - v} - 4 = - 3$

Step 2

Move all terms not containing $\sqrt{- 3 - v}$ to the right side of the equation.

Add $4$ to both sides of the equation.

$\sqrt{- 3 - v} = - 3 + 4$

Add $- 3$ and $4$ .

$\sqrt{- 3 - v} = 1$

Step 3

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

${\sqrt{- 3 - v}}^{2} = 1^{2}$

Step 4

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$- 3 - v = 1^{2}$

Simplify the right side.

One to any power is one.

$- 3 - v = 1$

Step 5

Solve for $v$ .

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

Add $3$ to both sides of the equation.

$- v = 1 + 3$

Add $1$ and $3$ .

$- v = 4$

Divide each term in $- v = 4$ by $- 1$ and simplify.

Divide each term in $- v = 4$ by $- 1$ .

$\frac{- v}{- 1} = \frac{4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{v}{1} = \frac{4}{- 1}$

Divide $v$ by $1$ .

$v = \frac{4}{- 1}$

Simplify the right side.

Divide $4$ by $- 1$ .

$v = - 4$

Solve for v -3 = square root of -3-v-4

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