Solve by Factoring square root of 2x-5-1=2

$\sqrt{2 x - 5} - 1 = 2$

Step 1

Subtract $2$ from both sides of the equation.

$\sqrt{2 x - 5} - 1 - 2 = 0$

Step 2

Subtract $2$ from $- 1$ .

$\sqrt{2 x - 5} - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$\sqrt{2 x - 5} = 3$

Step 4

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

${\sqrt{2 x - 5}}^{2} = 3^{2}$

Step 5

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x - 5}$ as ${(2 x - 5)}^{\frac{1}{2}}$ .

${({(2 x - 5)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(2 x - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x - 5)}^{\frac{1}{2}})}^{2}$ .

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

${(2 x - 5)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x - 5)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(2 x - 5)}^{1} = 3^{2}$

Simplify.

$2 x - 5 = 3^{2}$

Simplify the right side.

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

$2 x - 5 = 9$

Step 6

Solve for $x$ .

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

Add $5$ to both sides of the equation.

$2 x = 9 + 5$

Add $9$ and $5$ .

$2 x = 14$

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$

Solve by Factoring square root of 2x-5-1=2

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