Algebra Examples

$y = x^{2} - 4$ $y = 5$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} - 4 = 5$

Step 2

Solve $x^{2} - 4 = 5$ for $x$ .

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Step 2.1

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

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Step 2.1.1

Add $4$ to both sides of the equation.

$x^{2} = 5 + 4$

Step 2.1.2

Add $5$ and $4$ .

$x^{2} = 9$

Step 2.2

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

$x = \pm \sqrt{9}$

Step 2.3

Simplify $\pm \sqrt{9}$ .

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Step 2.3.1

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

$x = \pm \sqrt{3^{2}}$

Step 2.3.2

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

$x = \pm 3$

Step 2.4

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

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Step 2.4.1

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

$x = 3$

Step 2.4.2

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

$x = - 3$

Step 2.4.3

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

$x = 3, - 3$

Step 3

Substitute $3$ for $x$ .

$y = 5$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(3, 5)$

$(- 3, 5)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(3, 5), (- 3, 5)$

Equation Form:

$x = 3, y = 5$

$x = - 3, y = 5$

Step 6