Precalculus Examples

$x^{2} - 3 x = 12 - 3 (x - 2)$

Step 1

Simplify $12 - 3 (x - 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$x^{2} - 3 x = 12 - 3 x - 3 \cdot - 2$

Step 1.1.2

Multiply $- 3$ by $- 2$ .

$x^{2} - 3 x = 12 - 3 x + 6$

Step 1.2

Add $12$ and $6$ .

$x^{2} - 3 x = - 3 x + 18$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Add $3 x$ to both sides of the equation.

$x^{2} - 3 x + 3 x = 18$

Step 2.2

Combine the opposite terms in $x^{2} - 3 x + 3 x$ .

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Step 2.2.1

Add $- 3 x$ and $3 x$ .

$x^{2} + 0 = 18$

Step 2.2.2

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

$x^{2} = 18$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{18}$

Step 4

Simplify $\pm \sqrt{18}$ .

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Step 4.1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 4.1.1

Factor $9$ out of $18$ .

$x = \pm \sqrt{9 (2)}$

Step 4.1.2

Rewrite $9$ as $3^{2}$ .

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

Step 4.2

Pull terms out from under the radical.

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

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 3 \sqrt{2}$

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3 \sqrt{2}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

Decimal Form:

$x = 4.24264068 \dots, - 4.24264068 \dots$