Calculus Examples

$f (x) = {(x - 2)}^{2} - 1$

Step 1

Set ${(x - 2)}^{2} - 1$ equal to $0$ .

${(x - 2)}^{2} - 1 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $1$ to both sides of the equation.

${(x - 2)}^{2} = 1$

Step 2.2

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

$x - 2 = \pm \sqrt{1}$

Step 2.3

Any root of $1$ is $1$ .

$x - 2 = \pm 1$

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.

$x - 2 = 1$

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 $2$ to both sides of the equation.

$x = 1 + 2$

Step 2.4.2.2

Add $1$ and $2$ .

$x = 3$

Step 2.4.3

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

$x - 2 = - 1$

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 $2$ to both sides of the equation.

$x = - 1 + 2$

Step 2.4.4.2

Add $- 1$ and $2$ .

$x = 1$

Step 2.4.5

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

$x = 3, 1$

Step 3