Calculus Examples

y = x^{2} - 144

$y = x^{2} - 144$

Step 1

Set

x^{2} - 144

$x^{2} - 144$ equal to

0

$0$ .

x^{2} - 144 = 0

$x^{2} - 144 = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Add

144

$144$ to both sides of the equation.

x^{2} = 144

$x^{2} = 144$

Step 2.2

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

x = \pm \sqrt{144}

$x = \pm \sqrt{144}$

Step 2.3

Simplify

\pm \sqrt{144}

$\pm \sqrt{144}$ .

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Step 2.3.1

Rewrite

144

$144$ as

12^{2}

$12^{2}$ .

x = \pm \sqrt{12^{2}}

$x = \pm \sqrt{12^{2}}$

Step 2.3.2

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

x = \pm 12

$x = \pm 12$

x = \pm 12

$x = \pm 12$

Step 2.4

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

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Step 2.4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

x = 12

$x = 12$

Step 2.4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - 12

$x = - 12$

Step 2.4.3

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

x = 12, - 12

$x = 12, - 12$

x = 12, - 12

$x = 12, - 12$

Step 2.5

The multiplicity of a root is the number of times the root appears. For example, a factor of

{(x + 5)}^{3}

${(x + 5)}^{3}$ would have a root at

x = - 5

$x = - 5$ with multiplicity of

3

$3$ .

x = 12

$x = 12$ (Multiplicity of

1

$1$ )

x = - 12

$x = - 12$ (Multiplicity of

1

$1$ )

x = 12

$x = 12$ (Multiplicity of

1

$1$ )

x = - 12

$x = - 12$ (Multiplicity of

1

$1$ )

Step 3

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