Basic Math Examples

$(s - 2) (s - 9) = 4$

Step 1

Simplify $(s - 2) (s - 9)$ .

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Step 1.1

Expand $(s - 2) (s - 9)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$s (s - 9) - 2 (s - 9) = 4$

Step 1.1.2

Apply the distributive property.

$s \cdot s + s \cdot - 9 - 2 (s - 9) = 4$

Step 1.1.3

Apply the distributive property.

$s \cdot s + s \cdot - 9 - 2 s - 2 \cdot - 9 = 4$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $s$ by $s$ .

$s^{2} + s \cdot - 9 - 2 s - 2 \cdot - 9 = 4$

Step 1.2.1.2

Move $- 9$ to the left of $s$ .

$s^{2} - 9 \cdot s - 2 s - 2 \cdot - 9 = 4$

Step 1.2.1.3

Multiply $- 2$ by $- 9$ .

$s^{2} - 9 s - 2 s + 18 = 4$

Step 1.2.2

Subtract $2 s$ from $- 9 s$ .

$s^{2} - 11 s + 18 = 4$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the equation.

$s^{2} - 11 s + 18 - 4 = 0$

Step 2.2

Subtract $4$ from $18$ .

$s^{2} - 11 s + 14 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 1$ , $b = - 11$ , and $c = 14$ into the quadratic formula and solve for $s$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (1 \cdot 14)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 11$ to the power of $2$ .

$s = \frac{11 \pm \sqrt{121 - 4 \cdot 1 \cdot 14}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot 14$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$s = \frac{11 \pm \sqrt{121 - 4 \cdot 14}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $14$ .

$s = \frac{11 \pm \sqrt{121 - 56}}{2 \cdot 1}$

Step 5.1.3

Subtract $56$ from $121$ .

$s = \frac{11 \pm \sqrt{65}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$s = \frac{11 \pm \sqrt{65}}{2}$

Step 6

The final answer is the combination of both solutions.

$s = \frac{11 + \sqrt{65}}{2}, \frac{11 - \sqrt{65}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$s = \frac{11 + \sqrt{65}}{2}, \frac{11 - \sqrt{65}}{2}$

Decimal Form:

$s = 9.53112887 \dots, 1.46887112 \dots$