Trigonometry Examples

$2 + {(4 x - 4)}^{\frac{1}{2}} = 6$

Step 1

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

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Step 1.1

Subtract $2$ from both sides of the equation.

${(4 x - 4)}^{\frac{1}{2}} = 6 - 2$

Step 1.2

Subtract $2$ from $6$ .

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

Step 2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

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

Step 3.1.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

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

Step 3.1.1.1.2.2

Rewrite the expression.

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

Step 3.1.1.2

Simplify.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $4$ to the power of $2$ .

$4 x - 4 = 16$

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 $4$ to both sides of the equation.

$4 x = 16 + 4$

Step 4.1.2

Add $16$ and $4$ .

$4 x = 20$

Step 4.2

Divide each term in $4 x = 20$ by $4$ and simplify.

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Step 4.2.1

Divide each term in $4 x = 20$ by $4$ .

$\frac{4 x}{4} = \frac{20}{4}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{20}{4}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{4}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $20$ by $4$ .

$x = 5$