Calculus Examples

$12 x^{2} - 12 = 0$

Step 1

Add $12$ to both sides of the equation.

$12 x^{2} = 12$

Step 2

Divide each term in $12 x^{2} = 12$ by $12$ and simplify.

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Step 2.1

Divide each term in $12 x^{2} = 12$ by $12$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $12$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

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

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $12$ by $12$ .

$x^{2} = 1$

Step 3

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

$x = \pm \sqrt{1}$

Step 4

Any root of $1$ is $1$ .

$x = \pm 1$

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.

$x = 1$

Step 5.2

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

$x = - 1$

Step 5.3

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

$x = 1, - 1$