Algebra Examples

$7 x^{2} + 1 = 0$

Step 1

Subtract $1$ from both sides of the equation.

$7 x^{2} = - 1$

Step 2

Divide each term in $7 x^{2} = - 1$ by $7$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $7 x^{2} = - 1$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{- 1}{7}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{- 1}{7}$

Step 2.2.1.2

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

$x^{2} = \frac{- 1}{7}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Move the negative in front of the fraction.

$x^{2} = - \frac{1}{7}$

Step 3

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

$x = \pm \sqrt{- \frac{1}{7}}$

Step 4

Simplify $\pm \sqrt{- \frac{1}{7}}$ .

Tap for more steps...

Step 4.1

Rewrite $- \frac{1}{7}$ as $i^{2} \frac{1^{2}}{7}$ .

Tap for more steps...

Step 4.1.1

Rewrite $- 1$ as $i^{2}$ .

$x = \pm \sqrt{i^{2} \frac{1}{7}}$

Step 4.1.2

Rewrite $1$ as $1^{2}$ .

$x = \pm \sqrt{i^{2} \frac{1^{2}}{7}}$

Step 4.2

Pull terms out from under the radical.

$x = \pm i \sqrt{\frac{1^{2}}{7}}$

Step 4.3

One to any power is one.

$x = \pm i \sqrt{\frac{1}{7}}$

Step 4.4

Rewrite $\sqrt{\frac{1}{7}}$ as $\frac{\sqrt{1}}{\sqrt{7}}$ .

$x = \pm i \frac{\sqrt{1}}{\sqrt{7}}$

Step 4.5

Any root of $1$ is $1$ .

$x = \pm i \frac{1}{\sqrt{7}}$

Step 4.6

Multiply $\frac{1}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = \pm i (\frac{1}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}})$

Step 4.7

Combine and simplify the denominator.

Tap for more steps...

Step 4.7.1

Multiply $\frac{1}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$x = \pm i \frac{\sqrt{7}}{\sqrt{7} \sqrt{7}}$

Step 4.7.2

Raise $\sqrt{7}$ to the power of $1$ .

$x = \pm i \frac{\sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Step 4.7.3

Raise $\sqrt{7}$ to the power of $1$ .

$x = \pm i \frac{\sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

Step 4.7.4

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

$x = \pm i \frac{\sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Step 4.7.5

Add $1$ and $1$ .

$x = \pm i \frac{\sqrt{7}}{{\sqrt{7}}^{2}}$

Step 4.7.6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Tap for more steps...

Step 4.7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$x = \pm i \frac{\sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

Step 4.7.6.2

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

$x = \pm i \frac{\sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

Step 4.7.6.3

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

$x = \pm i \frac{\sqrt{7}}{7^{\frac{2}{2}}}$

Step 4.7.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.7.6.4.1

Cancel the common factor.

$x = \pm i \frac{\sqrt{7}}{7^{\frac{2}{2}}}$

Step 4.7.6.4.2

Rewrite the expression.

$x = \pm i \frac{\sqrt{7}}{7^{1}}$

Step 4.7.6.5

Evaluate the exponent.

$x = \pm i \frac{\sqrt{7}}{7}$

Step 4.8

Combine $i$ and $\frac{\sqrt{7}}{7}$ .

$x = \pm \frac{i \sqrt{7}}{7}$

Step 5

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

Tap for more steps...

Step 5.1

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

$x = \frac{i \sqrt{7}}{7}$

Step 5.2

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

$x = - \frac{i \sqrt{7}}{7}$

Step 5.3

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

$x = \frac{i \sqrt{7}}{7}, - \frac{i \sqrt{7}}{7}$

Step 6