Solve by Factoring square root of 1-3x=-7

$\sqrt{1 - 3 x} = - 7$

Step 1

Add $7$ to both sides of the equation.

$\sqrt{1 - 3 x} + 7 = 0$

Step 2

Subtract $7$ from both sides of the equation.

$\sqrt{1 - 3 x} = - 7$

Step 3

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

${\sqrt{1 - 3 x}}^{2} = {(- 7)}^{2}$

Step 4

Simplify each side of the equation.

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

${({(1 - 3 x)}^{\frac{1}{2}})}^{2} = {(- 7)}^{2}$

Simplify the left side.

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

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

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

${(1 - 3 x)}^{\frac{1}{2} \cdot 2} = {(- 7)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(1 - 3 x)}^{\frac{1}{2} \cdot 2} = {(- 7)}^{2}$

Rewrite the expression.

${(1 - 3 x)}^{1} = {(- 7)}^{2}$

Simplify.

$1 - 3 x = {(- 7)}^{2}$

Simplify the right side.

Raise $- 7$ to the power of $2$ .

$1 - 3 x = 49$

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.

$- 3 x = 49 - 1$

Subtract $1$ from $49$ .

$- 3 x = 48$

Divide each term in $- 3 x = 48$ by $- 3$ and simplify.

Divide each term in $- 3 x = 48$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{48}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{48}{- 3}$

Divide $x$ by $1$ .

$x = \frac{48}{- 3}$

Simplify the right side.

Divide $48$ by $- 3$ .

$x = - 16$

Step 6

Exclude the solutions that do not make $\sqrt{1 - 3 x} + 7 = 0$ true.

$No solution$

Solve by Factoring square root of 1-3x=-7

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