Finite Math Examples

${(x + 2)}^{2} = 9$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Subtract $9$ from both sides of the equation.

${(x + 2)}^{2} - 9 = 0$

Step 1.2

Simplify ${(x + 2)}^{2} - 9$ .

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite ${(x + 2)}^{2}$ as $(x + 2) (x + 2)$ .

$(x + 2) (x + 2) - 9 = 0$

Step 1.2.1.2

Expand $(x + 2) (x + 2)$ using the FOIL Method.

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Step 1.2.1.2.1

Apply the distributive property.

$x (x + 2) + 2 (x + 2) - 9 = 0$

Step 1.2.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 (x + 2) - 9 = 0$

Step 1.2.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2 - 9 = 0$

Step 1.2.1.3

Simplify and combine like terms.

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Step 1.2.1.3.1

Simplify each term.

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Step 1.2.1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 2 + 2 x + 2 \cdot 2 - 9 = 0$

Step 1.2.1.3.1.2

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

$x^{2} + 2 \cdot x + 2 x + 2 \cdot 2 - 9 = 0$

Step 1.2.1.3.1.3

Multiply $2$ by $2$ .

$x^{2} + 2 x + 2 x + 4 - 9 = 0$

Step 1.2.1.3.2

Add $2 x$ and $2 x$ .

$x^{2} + 4 x + 4 - 9 = 0$

Step 1.2.2

Subtract $9$ from $4$ .

$x^{2} + 4 x - 5 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 4$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (1 \cdot - 5)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 5}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 5$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 5}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 5$ .

$x = \frac{- 4 \pm \sqrt{16 + 20}}{2 \cdot 1}$

Step 4.1.3

Add $16$ and $20$ .

$x = \frac{- 4 \pm \sqrt{36}}{2 \cdot 1}$

Step 4.1.4

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 4 \pm \sqrt{6^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$x = \frac{- 4 \pm 6}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 4 \pm 6}{2}$

Step 4.3

Simplify $\frac{- 4 \pm 6}{2}$ .

$x = - 2 \pm 3$

Step 5

The final answer is the combination of both solutions.

$x = 1, - 5$