Algebra Examples

$2 x - x (2 - x) = 12$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $2 x - x (2 - x)$ .

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Step 1.1.1.1

Simplify each term.

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Step 1.1.1.1.1

Apply the distributive property.

$2 x - x \cdot 2 - x (- x) = 12$

Step 1.1.1.1.2

Multiply $2$ by $- 1$ .

$2 x - 2 x - x (- x) = 12$

Step 1.1.1.1.3

Rewrite using the commutative property of multiplication.

$2 x - 2 x - 1 \cdot - 1 x \cdot x = 12$

Step 1.1.1.1.4

Simplify each term.

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Step 1.1.1.1.4.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.1.1.4.1.1

Move $x$ .

$2 x - 2 x - 1 \cdot - 1 (x \cdot x) = 12$

Step 1.1.1.1.4.1.2

Multiply $x$ by $x$ .

$2 x - 2 x - 1 \cdot - 1 x^{2} = 12$

Step 1.1.1.1.4.2

Multiply $- 1$ by $- 1$ .

$2 x - 2 x + 1 x^{2} = 12$

Step 1.1.1.1.4.3

Multiply $x^{2}$ by $1$ .

$2 x - 2 x + x^{2} = 12$

Step 1.1.1.2

Simplify by adding terms.

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Step 1.1.1.2.1

Subtract $2 x$ from $2 x$ .

$0 + x^{2} = 12$

Step 1.1.1.2.2

Add $0$ and $x^{2}$ .

$x^{2} = 12$

Step 1.2

Subtract $12$ from both sides of the equation.

$x^{2} - 12 = 0$

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 $a = 1$ , $b = 0$ , and $c = - 12$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 12)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 12}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 12$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 12}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 12$ .

$x = \frac{0 \pm \sqrt{0 + 48}}{2 \cdot 1}$

Step 4.1.3

Add $0$ and $48$ .

$x = \frac{0 \pm \sqrt{48}}{2 \cdot 1}$

Step 4.1.4

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 4.1.4.1

Factor $16$ out of $48$ .

$x = \frac{0 \pm \sqrt{16 (3)}}{2 \cdot 1}$

Step 4.1.4.2

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2} \cdot 3}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{0 \pm 4 \sqrt{3}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{0 \pm 4 \sqrt{3}}{2}$

Step 4.3

Simplify $\frac{0 \pm 4 \sqrt{3}}{2}$ .

$x = \pm 2 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{3}$

Decimal Form:

$x = 3.46410161 \dots, - 3.46410161 \dots$