Algebra Examples

$\frac{1}{4} (8 x - 4^{2}) = 0$

Step 1

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cdot (8 x - 4^{2})) = 4 \cdot 0$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $4 (\frac{1}{4} \cdot (8 x - 4^{2}))$ .

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

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

$4 (\frac{1}{4} \cdot (8 x - 1 \cdot 16)) = 4 \cdot 0$

Step 2.1.1.1.2

Multiply $- 1$ by $16$ .

$4 (\frac{1}{4} \cdot (8 x - 16)) = 4 \cdot 0$

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

Apply the distributive property.

$4 (\frac{1}{4} (8 x) + \frac{1}{4} \cdot - 16) = 4 \cdot 0$

Step 2.1.1.2.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.2.1

Factor $4$ out of $8 x$ .

$4 (\frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 16) = 4 \cdot 0$

Step 2.1.1.2.2.2

Cancel the common factor.

$4 (\frac{1}{4} (4 (2 x)) + \frac{1}{4} \cdot - 16) = 4 \cdot 0$

Step 2.1.1.2.2.3

Rewrite the expression.

$4 (2 x + \frac{1}{4} \cdot - 16) = 4 \cdot 0$

Step 2.1.1.2.3

Cancel the common factor of $4$ .

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Step 2.1.1.2.3.1

Factor $4$ out of $- 16$ .

$4 (2 x + \frac{1}{4} \cdot (4 (- 4))) = 4 \cdot 0$

Step 2.1.1.2.3.2

Cancel the common factor.

$4 (2 x + \frac{1}{4} \cdot (4 \cdot - 4)) = 4 \cdot 0$

Step 2.1.1.2.3.3

Rewrite the expression.

$4 (2 x - 4) = 4 \cdot 0$

Step 2.1.1.2.4

Apply the distributive property.

$4 (2 x) + 4 \cdot - 4 = 4 \cdot 0$

Step 2.1.1.2.5

Multiply.

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Step 2.1.1.2.5.1

Multiply $2$ by $4$ .

$8 x + 4 \cdot - 4 = 4 \cdot 0$

Step 2.1.1.2.5.2

Multiply $4$ by $- 4$ .

$8 x - 16 = 4 \cdot 0$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $4$ by $0$ .

$8 x - 16 = 0$

Step 3

Add $16$ to both sides of the equation.

$8 x = 16$

Step 4

Divide each term in $8 x = 16$ by $8$ and simplify.

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Step 4.1

Divide each term in $8 x = 16$ by $8$ .

$\frac{8 x}{8} = \frac{16}{8}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $8$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{16}{8}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{16}{8}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $16$ by $8$ .

$x = 2$