Solve by Factoring square root of 2x-1-3=0

$\sqrt{2 x - 1} - 3 = 0$

Step 1

Add $3$ to both sides of the equation.

$\sqrt{2 x - 1} = 3$

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$2 x - 1 = 9$

Step 4

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$2 x = 9 + 1$

Add $9$ and $1$ .

$2 x = 10$

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$