Basic Math Examples

$q + q^{2} = 10$

Step 1

Subtract $10$ from both sides of the equation.

$q + q^{2} - 10 = 0$

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 $c = - 10$ into the quadratic formula and solve for $q$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot - 10)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

One to any power is one.

$q = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 10}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 10$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$q = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 10}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 10$ .

$q = \frac{- 1 \pm \sqrt{1 + 40}}{2 \cdot 1}$

Step 4.1.3

Add $1$ and $40$ .

$q = \frac{- 1 \pm \sqrt{41}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$q = \frac{- 1 \pm \sqrt{41}}{2}$

Step 5

The final answer is the combination of both solutions.

$q = - \frac{1 - \sqrt{41}}{2}, - \frac{1 + \sqrt{41}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$q = - \frac{1 - \sqrt{41}}{2}, - \frac{1 + \sqrt{41}}{2}$

Decimal Form:

$q = 2.70156211 \dots, - 3.70156211 \dots$