Algebra Examples

$4 a^{2} - b^{2} = 0$

Step 1

Subtract $4 a^{2}$ from both sides of the equation.

$- b^{2} = - 4 a^{2}$

Step 2

Divide each term in $- b^{2} = - 4 a^{2}$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- b^{2} = - 4 a^{2}$ by $- 1$ .

$\frac{- b^{2}}{- 1} = \frac{- 4 a^{2}}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{b^{2}}{1} = \frac{- 4 a^{2}}{- 1}$

Step 2.2.2

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

$b^{2} = \frac{- 4 a^{2}}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of $\frac{- 4 a^{2}}{- 1}$ .

$b^{2} = - 1 \cdot (- 4 a^{2})$

Step 2.3.2

Rewrite $- 1 \cdot (- 4 a^{2})$ as $- (- 4 a^{2})$ .

$b^{2} = - (- 4 a^{2})$

Step 2.3.3

Multiply $- 4$ by $- 1$ .

$b^{2} = 4 a^{2}$

Step 3

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

$b = \pm \sqrt{4 a^{2}}$

Step 4

Simplify $\pm \sqrt{4 a^{2}}$ .

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Step 4.1

Rewrite $4 a^{2}$ as ${(2 a)}^{2}$ .

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

Step 4.2

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

$b = \pm 2 a$

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.

$b = 2 a$

Step 5.2

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

$b = - 2 a$

Step 5.3

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

$b = 2 a$

$b = - 2 a$

$b = 2 a$

$b = - 2 a$