Finite Math Examples

$g (x) = {(x - 3)}^{2} - 4$

Step 1

Set ${(x - 3)}^{2} - 4$ equal to $0$ .

${(x - 3)}^{2} - 4 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $4$ to both sides of the equation.

${(x - 3)}^{2} = 4$

Step 2.2

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

$x - 3 = \pm \sqrt{4}$

Step 2.3

Simplify $\pm \sqrt{4}$ .

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Step 2.3.1

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

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

Step 2.3.2

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

$x - 3 = \pm 2$

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.

$x - 3 = 2$

Step 2.4.2

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

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Step 2.4.2.1

Add $3$ to both sides of the equation.

$x = 2 + 3$

Step 2.4.2.2

Add $2$ and $3$ .

$x = 5$

Step 2.4.3

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

$x - 3 = - 2$

Step 2.4.4

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

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Step 2.4.4.1

Add $3$ to both sides of the equation.

$x = - 2 + 3$

Step 2.4.4.2

Add $- 2$ and $3$ .

$x = 1$

Step 2.4.5

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

$x = 5, 1$

Step 3