Solve for j 4j^2-81=0

$4 j^{2} - 81 = 0$

Step 1

Add $81$ to both sides of the equation.

$4 j^{2} = 81$

Step 2

Divide each term in $4 j^{2} = 81$ by $4$ and simplify.

Divide each term in $4 j^{2} = 81$ by $4$ .

$\frac{4 j^{2}}{4} = \frac{81}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 j^{2}}{4} = \frac{81}{4}$

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

$j^{2} = \frac{81}{4}$

Step 3

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

$j = \pm \sqrt{\frac{81}{4}}$

Step 4

Simplify $\pm \sqrt{\frac{81}{4}}$ .

Rewrite $\sqrt{\frac{81}{4}}$ as $\frac{\sqrt{81}}{\sqrt{4}}$ .

$j = \pm \frac{\sqrt{81}}{\sqrt{4}}$

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

$j = \pm \frac{\sqrt{9^{2}}}{\sqrt{4}}$

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

$j = \pm \frac{9}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$j = \pm \frac{9}{\sqrt{2^{2}}}$

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

$j = \pm \frac{9}{2}$

Step 5

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

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

$j = \frac{9}{2}$

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

$j = - \frac{9}{2}$

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

$j = \frac{9}{2}, - \frac{9}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$j = \frac{9}{2}, - \frac{9}{2}$

Decimal Form:

$j = 4.5, - 4.5$

Mixed Number Form:

$j = 4 \frac{1}{2}, - 4 \frac{1}{2}$

Solve for j 4j^2-81=0

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