Solve for j 5j^2-9=0

$5 j^{2} - 9 = 0$

Add $9$ to both sides of the equation.

$5 j^{2} = 9$

Divide each term in $5 j^{2} = 9$ by $5$ and simplify.

Divide each term in $5 j^{2} = 9$ by $5$ .

$\frac{5 j^{2}}{5} = \frac{9}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 j^{2}}{5} = \frac{9}{5}$

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

$j^{2} = \frac{9}{5}$

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

$j = \pm \sqrt{\frac{9}{5}}$

Simplify $\pm \sqrt{\frac{9}{5}}$ .

Rewrite $\sqrt{\frac{9}{5}}$ as $\frac{\sqrt{9}}{\sqrt{5}}$ .

$j = \pm \frac{\sqrt{9}}{\sqrt{5}}$

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$j = \pm \frac{\sqrt{3^{2}}}{\sqrt{5}}$

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

$j = \pm \frac{3}{\sqrt{5}}$

Multiply $\frac{3}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$j = \pm \frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Combine and simplify the denominator.

Multiply $\frac{3}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$j = \pm \frac{3 \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$j = \pm \frac{3 \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$j = \pm \frac{3 \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$j = \pm \frac{3 \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$j = \pm \frac{3 \sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$j = \pm \frac{3 \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$j = \pm \frac{3 \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$j = \pm \frac{3 \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$j = \pm \frac{3 \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$j = \pm \frac{3 \sqrt{5}}{5^{1}}$

Evaluate the exponent.

$j = \pm \frac{3 \sqrt{5}}{5}$

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.

$j = \frac{3 \sqrt{5}}{5}$

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

$j = - \frac{3 \sqrt{5}}{5}$

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

$j = \frac{3 \sqrt{5}}{5}, - \frac{3 \sqrt{5}}{5}$

The result can be shown in multiple forms.

Exact Form:

$j = \frac{3 \sqrt{5}}{5}, - \frac{3 \sqrt{5}}{5}$

Decimal Form:

$j = 1.34164078 \dots, - 1.34164078 \dots$

Solve for j 5j^2-9=0

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