Algebra Examples

x (x - 6) = 0

$x (x - 6) = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify

x (x - 6)

$x (x - 6)$ .

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Step 1.1.1

Apply the distributive property.

x \cdot x + x \cdot - 6 = 0

$x \cdot x + x \cdot - 6 = 0$

Step 1.1.2

Simplify the expression.

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Step 1.1.2.1

Multiply

x

$x$ by

x

$x$ .

x^{2} + x \cdot - 6 = 0

$x^{2} + x \cdot - 6 = 0$

Step 1.1.2.2

Move

- 6

$- 6$ to the left of

x

$x$ .

x^{2} - 6 x = 0

$x^{2} - 6 x = 0$

x^{2} - 6 x = 0

$x^{2} - 6 x = 0$

x^{2} - 6 x = 0

$x^{2} - 6 x = 0$

x^{2} - 6 x = 0

$x^{2} - 6 x = 0$

Step 2

Use the quadratic formula to find the solutions.

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

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

Step 3

Substitute the values

a = 1

$a = 1$ ,

b = - 6

$b = - 6$ , and

c = 0

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

x

$x$ .

\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot 0)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise

- 6

$- 6$ to the power of

2

$2$ .

x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 0}}{2 \cdot 1}$

Step 4.1.2

Multiply

- 4 \cdot 1 \cdot 0

$- 4 \cdot 1 \cdot 0$ .

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Step 4.1.2.1

Multiply

- 4

$- 4$ by

1

$1$ .

x = \frac{6 \pm \sqrt{36 - 4 \cdot 0}}{2 \cdot 1}

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 0}}{2 \cdot 1}$

Step 4.1.2.2

Multiply

- 4

$- 4$ by

0

$0$ .

x = \frac{6 \pm \sqrt{36 + 0}}{2 \cdot 1}

$x = \frac{6 \pm \sqrt{36 + 0}}{2 \cdot 1}$

x = \frac{6 \pm \sqrt{36 + 0}}{2 \cdot 1}

$x = \frac{6 \pm \sqrt{36 + 0}}{2 \cdot 1}$

Step 4.1.3

Add

36

$36$ and

0

$0$ .

x = \frac{6 \pm \sqrt{36}}{2 \cdot 1}

$x = \frac{6 \pm \sqrt{36}}{2 \cdot 1}$

Step 4.1.4

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

x = \frac{6 \pm \sqrt{6^{2}}}{2 \cdot 1}

$x = \frac{6 \pm \sqrt{6^{2}}}{2 \cdot 1}$

Step 4.1.5

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

x = \frac{6 \pm 6}{2 \cdot 1}

$x = \frac{6 \pm 6}{2 \cdot 1}$

x = \frac{6 \pm 6}{2 \cdot 1}

$x = \frac{6 \pm 6}{2 \cdot 1}$

Step 4.2

Multiply

2

$2$ by

1

$1$ .

x = \frac{6 \pm 6}{2}

$x = \frac{6 \pm 6}{2}$

Step 4.3

Simplify

\frac{6 \pm 6}{2}

$\frac{6 \pm 6}{2}$ .

x = 3 \pm 3

$x = 3 \pm 3$

x = 3 \pm 3

$x = 3 \pm 3$

Step 5

The final answer is the combination of both solutions.

x = 6, 0

$x = 6, 0$