Precalculus Examples

a^{2} x^{2} - b^{2} = 0

$a^{2} x^{2} - b^{2} = 0$

Step 1

Add

$b^{2}$ to both sides of the equation.

$a^{2} x^{2} = b^{2}$

Step 2

Divide each term in

$a^{2} x^{2} = b^{2}$ by

$a^{2}$ and simplify.

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Step 2.1

Divide each term in

$a^{2} x^{2} = b^{2}$ by

$a^{2}$ .

$\frac{a^{2} x^{2}}{a^{2}} = \frac{b^{2}}{a^{2}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

$a^{2}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a^{2} x^{2}}{a^{2}} = \frac{b^{2}}{a^{2}}$

Step 2.2.1.2

Divide

$x^{2}$ by

$1$ .

$x^{2} = \frac{b^{2}}{a^{2}}$

Step 3

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

$x = \pm \sqrt{\frac{b^{2}}{a^{2}}}$

Step 4

Simplify

$\pm \sqrt{\frac{b^{2}}{a^{2}}}$ .

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Step 4.1

Rewrite

$\frac{b^{2}}{a^{2}}$ as

${(\frac{b}{a})}^{2}$ .

$x = \pm \sqrt{{(\frac{b}{a})}^{2}}$

Step 4.2

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

$x = \pm \frac{b}{a}$

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.

$x = \frac{b}{a}$

Step 5.2

Next, use the negative value of the

$\pm$ to find the second solution.

$x = - \frac{b}{a}$

Step 5.3

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

$x = \frac{b}{a}$

$x = - \frac{b}{a}$

$x = \frac{b}{a}$

$x = - \frac{b}{a}$

$a^{2} x^{2} - b^{2} = 0$

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