Finite Math Examples

$f (x) = {(x - 1)}^{2} + 4$

Step 1

Set ${(x - 1)}^{2} + 4$ equal to $0$ .

${(x - 1)}^{2} + 4 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $4$ from both sides of the equation.

${(x - 1)}^{2} = - 4$

Step 2.2

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

$x - 1 = \pm \sqrt{- 4}$

Step 2.3

Simplify $\pm \sqrt{- 4}$ .

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Step 2.3.1

Rewrite $- 4$ as $- 1 (4)$ .

$x - 1 = \pm \sqrt{- 1 (4)}$

Step 2.3.2

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$x - 1 = \pm \sqrt{- 1} \cdot \sqrt{4}$

Step 2.3.3

Rewrite $\sqrt{- 1}$ as $i$ .

$x - 1 = \pm i \cdot \sqrt{4}$

Step 2.3.4

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

$x - 1 = \pm i \cdot \sqrt{2^{2}}$

Step 2.3.5

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

$x - 1 = \pm i \cdot 2$

Step 2.3.6

Move $2$ to the left of $i$ .

$x - 1 = \pm 2 i$

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.

$x - 1 = 2 i$

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 $1$ to both sides of the equation.

$x = 2 i + 1$

Step 2.4.2.2

Reorder $2 i$ and $1$ .

$x = 1 + 2 i$

Step 2.4.3

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

$x - 1 = - 2 i$

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 $1$ to both sides of the equation.

$x = - 2 i + 1$

Step 2.4.4.2

Reorder $- 2 i$ and $1$ .

$x = 1 - 2 i$

Step 2.4.5

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

$x = 1 + 2 i, 1 - 2 i$

Step 3