Algebra Examples

$x (x - 4) = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify

$x (x - 4)$ .

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Simplify the expression.

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Step 1.1.2.1

Multiply

$x$ by

$x$ .

$x^{2} + x \cdot - 4 = 0$

Step 1.1.2.2

Move

$- 4$ to the left of

$x$ .

$x^{2} - 4 x = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values

$a = 1$ ,

$b = - 4$ , and

$c = 0$ into the quadratic formula and solve for

$x$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise

$- 4$ to the power of

$2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Step 4.1.2

Multiply

$- 4 \cdot 1 \cdot 0$ .

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Step 4.1.2.1

Multiply

$- 4$ by

$1$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 0}}{2 \cdot 1}$

Step 4.1.2.2

Multiply

$- 4$ by

$0$ .

$x = \frac{4 \pm \sqrt{16 + 0}}{2 \cdot 1}$

Step 4.1.3

Add

$16$ and

$0$ .

$x = \frac{4 \pm \sqrt{16}}{2 \cdot 1}$

Step 4.1.4

Rewrite

$16$ as

$4^{2}$ .

$x = \frac{4 \pm \sqrt{4^{2}}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{4 \pm 4}{2 \cdot 1}$

Step 4.2

Multiply

$2$ by

$1$ .

$x = \frac{4 \pm 4}{2}$

Step 4.3

Simplify

$\frac{4 \pm 4}{2}$ .

$x = 2 \pm 2$

Step 5

The final answer is the combination of both solutions.

$x = 4, 0$