Algebra Examples

$(x + 4) (x - 5) + 3 = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify $(x + 4) (x - 5) + 3$ .

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Expand $(x + 4) (x - 5)$ using the FOIL Method.

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Step 1.1.1.1.1

Apply the distributive property.

$x (x - 5) + 4 (x - 5) + 3 = 0$

Step 1.1.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 4 (x - 5) + 3 = 0$

Step 1.1.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 5 + 4 x + 4 \cdot - 5 + 3 = 0$

Step 1.1.1.2

Simplify and combine like terms.

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Step 1.1.1.2.1

Simplify each term.

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Step 1.1.1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 + 4 x + 4 \cdot - 5 + 3 = 0$

Step 1.1.1.2.1.2

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x + 4 x + 4 \cdot - 5 + 3 = 0$

Step 1.1.1.2.1.3

Multiply $4$ by $- 5$ .

$x^{2} - 5 x + 4 x - 20 + 3 = 0$

Step 1.1.1.2.2

Add $- 5 x$ and $4 x$ .

$x^{2} - x - 20 + 3 = 0$

Step 1.1.2

Add $- 20$ and $3$ .

$x^{2} - x - 17 = 0$

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 $a = 1$ , $b = - 1$ , and $c = - 17$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (1 \cdot - 17)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 17}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 17$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot - 17}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 17$ .

$x = \frac{1 \pm \sqrt{1 + 68}}{2 \cdot 1}$

Step 4.1.3

Add $1$ and $68$ .

$x = \frac{1 \pm \sqrt{69}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{1 \pm \sqrt{69}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{69}}{2}$

Decimal Form:

$x = 4.65331193 \dots, - 3.65331193 \dots$