Algebra Examples

$x^{2} + y^{2} - 4 = 0$

Step 1

Move all terms not containing $y$ to the right side of the equation.

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Step 1.1

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

$y^{2} - 4 = - x^{2}$

Step 1.2

Add $4$ to both sides of the equation.

$y^{2} = - x^{2} + 4$

Step 2

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

$y = \pm \sqrt{- x^{2} + 4}$

Step 3

Simplify $\pm \sqrt{- x^{2} + 4}$ .

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Step 3.1

Simplify the expression.

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Step 3.1.1

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

$y = \pm \sqrt{- x^{2} + 2^{2}}$

Step 3.1.2

Reorder $- x^{2}$ and $2^{2}$ .

$y = \pm \sqrt{2^{2} - x^{2}}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

$y = \pm \sqrt{(2 + x) (2 - x)}$

Step 4

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

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Step 4.1

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

$y = \sqrt{(2 + x) (2 - x)}$

Step 4.2

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

$y = - \sqrt{(2 + x) (2 - x)}$

Step 4.3

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

$y = \sqrt{(2 + x) (2 - x)}$

$y = - \sqrt{(2 + x) (2 - x)}$

$y = \sqrt{(2 + x) (2 - x)}$

$y = - \sqrt{(2 + x) (2 - x)}$