Algebra Examples

$\sqrt{7 x - 6} - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$\sqrt{7 x - 6} = 6$

Step 2

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

${\sqrt{7 x - 6}}^{2} = 6^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x - 6}$ as ${(7 x - 6)}^{\frac{1}{2}}$ .

${({(7 x - 6)}^{\frac{1}{2}})}^{2} = 6^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(7 x - 6)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(7 x - 6)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(7 x - 6)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(7 x - 6)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(7 x - 6)}^{1} = 6^{2}$

Step 3.2.1.2

Simplify.

$7 x - 6 = 6^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $6$ to the power of $2$ .

$7 x - 6 = 36$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $6$ to both sides of the equation.

$7 x = 36 + 6$

Step 4.1.2

Add $36$ and $6$ .

$7 x = 42$

Step 4.2

Divide each term in $7 x = 42$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 x = 42$ by $7$ .

$\frac{7 x}{7} = \frac{42}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{42}{7}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{42}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $42$ by $7$ .

$x = 6$