Algebra Examples

3 x^{2} = 12

$3 x^{2} = 12$

Step 1

Divide each term in

3 x^{2} = 12

$3 x^{2} = 12$ by

3

$3$ and simplify.

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Step 1.1

Divide each term in

3 x^{2} = 12

$3 x^{2} = 12$ by

3

$3$ .

\frac{3 x^{2}}{3} = \frac{12}{3}

$\frac{3 x^{2}}{3} = \frac{12}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of

3

$3$ .

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Step 1.2.1.1

Cancel the common factor.

\frac{3 x^{2}}{3} = \frac{12}{3}

$\frac{3 x^{2}}{3} = \frac{12}{3}$

Step 1.2.1.2

Divide

x^{2}

$x^{2}$ by

1

$1$ .

x^{2} = \frac{12}{3}

$x^{2} = \frac{12}{3}$

x^{2} = \frac{12}{3}

$x^{2} = \frac{12}{3}$

x^{2} = \frac{12}{3}

$x^{2} = \frac{12}{3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide

12

$12$ by

3

$3$ .

x^{2} = 4

$x^{2} = 4$

x^{2} = 4

$x^{2} = 4$

x^{2} = 4

$x^{2} = 4$

Step 2

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

x = \pm \sqrt{4}

$x = \pm \sqrt{4}$

Step 3

Simplify

\pm \sqrt{4}

$\pm \sqrt{4}$ .

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Step 3.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

x = \pm \sqrt{2^{2}}

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

Step 3.2

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

x = \pm 2

$x = \pm 2$

x = \pm 2

$x = \pm 2$

Step 4

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

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Step 4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

x = 2

$x = 2$

Step 4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - 2

$x = - 2$

Step 4.3

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

x = 2, - 2

$x = 2, - 2$

x = 2, - 2

$x = 2, - 2$

3 x^{2} = 12

$3 x^{2} = 12$

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