Solve by Factoring square root of 7-2x+5=8

$\sqrt{7 - 2 x} + 5 = 8$

Step 1

Subtract $8$ from both sides of the equation.

$\sqrt{7 - 2 x} + 5 - 8 = 0$

Step 2

Subtract $8$ from $5$ .

$\sqrt{7 - 2 x} - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$\sqrt{7 - 2 x} = 3$

Step 4

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

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

Step 5

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$7 - 2 x = 3^{2}$

Simplify the right side.

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

$7 - 2 x = 9$

Step 6

Solve for $x$ .

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

Subtract $7$ from both sides of the equation.

$- 2 x = 9 - 7$

Subtract $7$ from $9$ .

$- 2 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $2$ by $- 2$ .

$x = - 1$

Solve by Factoring square root of 7-2x+5=8

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