Solve by Factoring square root of 4x-13-1=0

$\sqrt{4 x - 13} - 1 = 0$

Step 1

Add $1$ to both sides of the equation.

$\sqrt{4 x - 13} = 1$

Step 2

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

${\sqrt{4 x - 13}}^{2} = 1^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x - 13}$ as ${(4 x - 13)}^{\frac{1}{2}}$ .

${({(4 x - 13)}^{\frac{1}{2}})}^{2} = 1^{2}$

Simplify the left side.

Simplify ${({(4 x - 13)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 x - 13)}^{\frac{1}{2}})}^{2}$ .

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

${(4 x - 13)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 x - 13)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Rewrite the expression.

${(4 x - 13)}^{1} = 1^{2}$

Simplify.

$4 x - 13 = 1^{2}$

Simplify the right side.

One to any power is one.

$4 x - 13 = 1$

Step 4

Solve for $x$ .

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

Add $13$ to both sides of the equation.

$4 x = 1 + 13$

Add $1$ and $13$ .

$4 x = 14$

Divide each term in $4 x = 14$ by $4$ and simplify.

Divide each term in $4 x = 14$ by $4$ .

$\frac{4 x}{4} = \frac{14}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{14}{4}$

Divide $x$ by $1$ .

$x = \frac{14}{4}$

Simplify the right side.

Cancel the common factor of $14$ and $4$ .

Factor $2$ out of $14$ .

$x = \frac{2 (7)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 7}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 7}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{7}{2}$

Solve by Factoring square root of 4x-13-1=0

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