Solve by Factoring square root of 1-7x=8

$\sqrt{1 - 7 x} = 8$

Step 1

Subtract $8$ from both sides of the equation.

$\sqrt{1 - 7 x} - 8 = 0$

Step 2

Add $8$ to both sides of the equation.

$\sqrt{1 - 7 x} = 8$

Step 3

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

${\sqrt{1 - 7 x}}^{2} = 8^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{1 - 7 x}$ as ${(1 - 7 x)}^{\frac{1}{2}}$ .

${({(1 - 7 x)}^{\frac{1}{2}})}^{2} = 8^{2}$

Simplify the left side.

Simplify ${({(1 - 7 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(1 - 7 x)}^{\frac{1}{2}})}^{2}$ .

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

${(1 - 7 x)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(1 - 7 x)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Rewrite the expression.

${(1 - 7 x)}^{1} = 8^{2}$

Simplify.

$1 - 7 x = 8^{2}$

Simplify the right side.

Raise $8$ to the power of $2$ .

$1 - 7 x = 64$

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.

$- 7 x = 64 - 1$

Subtract $1$ from $64$ .

$- 7 x = 63$

Divide each term in $- 7 x = 63$ by $- 7$ and simplify.

Divide each term in $- 7 x = 63$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{63}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{63}{- 7}$

Divide $x$ by $1$ .

$x = \frac{63}{- 7}$

Simplify the right side.

Divide $63$ by $- 7$ .

$x = - 9$

Solve by Factoring square root of 1-7x=8

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