Solve by Factoring square root of 8x-21-1=0

$\sqrt{8 x - 21} - 1 = 0$

Step 1

Add $1$ to both sides of the equation.

$\sqrt{8 x - 21} = 1$

Step 2

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

${\sqrt{8 x - 21}}^{2} = 1^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 x - 21}$ as ${(8 x - 21)}^{\frac{1}{2}}$ .

${({(8 x - 21)}^{\frac{1}{2}})}^{2} = 1^{2}$

Simplify the left side.

Simplify ${({(8 x - 21)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(8 x - 21)}^{\frac{1}{2}})}^{2}$ .

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

${(8 x - 21)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(8 x - 21)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Rewrite the expression.

${(8 x - 21)}^{1} = 1^{2}$

Simplify.

$8 x - 21 = 1^{2}$

Simplify the right side.

One to any power is one.

$8 x - 21 = 1$

Step 4

Solve for $x$ .

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

Add $21$ to both sides of the equation.

$8 x = 1 + 21$

Add $1$ and $21$ .

$8 x = 22$

Divide each term in $8 x = 22$ by $8$ and simplify.

Divide each term in $8 x = 22$ by $8$ .

$\frac{8 x}{8} = \frac{22}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{22}{8}$

Divide $x$ by $1$ .

$x = \frac{22}{8}$

Simplify the right side.

Cancel the common factor of $22$ and $8$ .

Factor $2$ out of $22$ .

$x = \frac{2 (11)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 11}{2 \cdot 4}$

Cancel the common factor.

$x = \frac{2 \cdot 11}{2 \cdot 4}$

Rewrite the expression.

$x = \frac{11}{4}$

Solve by Factoring square root of 8x-21-1=0

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