Calculus Examples

$e^{x} (x^{2} - 144) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$e^{x} = 0$

$x^{2} - 144 = 0$

Step 2

Set $e^{x}$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $e^{x}$ equal to $0$ .

$e^{x} = 0$

Step 2.2

Solve $e^{x} = 0$ for $x$ .

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Step 2.2.1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{x}) = \ln (0)$

Step 2.2.2

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 2.2.3

There is no solution for $e^{x} = 0$

No solution

Step 3

Set $x^{2} - 144$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x^{2} - 144$ equal to $0$ .

$x^{2} - 144 = 0$

Step 3.2

Solve $x^{2} - 144 = 0$ for $x$ .

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Step 3.2.1

Add $144$ to both sides of the equation.

$x^{2} = 144$

Step 3.2.2

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

$x = \pm \sqrt{144}$

Step 3.2.3

Simplify $\pm \sqrt{144}$ .

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Step 3.2.3.1

Rewrite $144$ as $12^{2}$ .

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

Step 3.2.3.2

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

$x = \pm 12$

Step 3.2.4

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

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Step 3.2.4.1

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

$x = 12$

Step 3.2.4.2

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

$x = - 12$

Step 3.2.4.3

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

$x = 12, - 12$

Step 4

The final solution is all the values that make $e^{x} (x^{2} - 144) = 0$ true.

$x = 12, - 12$