Algebra Examples

$\sqrt{8 x - 17} = 1$

Step 1

Subtract $1$ from both sides of the equation.

$\sqrt{8 x - 17} - 1 = 0$

Step 2

Add $1$ to both sides of the equation.

$\sqrt{8 x - 17} = 1$

Step 3

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

${\sqrt{8 x - 17}}^{2} = 1^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 x - 17}$ as ${(8 x - 17)}^{\frac{1}{2}}$ .

${({(8 x - 17)}^{\frac{1}{2}})}^{2} = 1^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${({(8 x - 17)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Multiply the exponents in ${({(8 x - 17)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1.1

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

${(8 x - 17)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

${(8 x - 17)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(8 x - 17)}^{1} = 1^{2}$

Step 4.2.1.2

Simplify.

$8 x - 17 = 1^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

One to any power is one.

$8 x - 17 = 1$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Add $17$ to both sides of the equation.

$8 x = 1 + 17$

Step 5.1.2

Add $1$ and $17$ .

$8 x = 18$

Step 5.2

Divide each term in $8 x = 18$ by $8$ and simplify.

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Step 5.2.1

Divide each term in $8 x = 18$ by $8$ .

$\frac{8 x}{8} = \frac{18}{8}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $8$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{18}{8}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{8}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Cancel the common factor of $18$ and $8$ .

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Step 5.2.3.1.1

Factor $2$ out of $18$ .

$x = \frac{2 (9)}{8}$

Step 5.2.3.1.2

Cancel the common factors.

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Step 5.2.3.1.2.1

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 9}{2 \cdot 4}$

Step 5.2.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 9}{2 \cdot 4}$

Step 5.2.3.1.2.3

Rewrite the expression.

$x = \frac{9}{4}$