Finite Math Examples

$x - x^{2} = 1 - 6 x^{2}$

Step 1

Move all terms containing $x$ to the left side of the equation.

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Step 1.1

Add $6 x^{2}$ to both sides of the equation.

$x - x^{2} + 6 x^{2} = 1$

Step 1.2

Add $- x^{2}$ and $6 x^{2}$ .

$x + 5 x^{2} = 1$

Step 2

Subtract $1$ from both sides of the equation.

$x + 5 x^{2} - 1 = 0$

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

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

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

One to any power is one.

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

Step 5.1.2

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

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Step 5.1.2.1

Multiply $- 4$ by $5$ .

$x = \frac{- 1 \pm \sqrt{1 - 20 \cdot - 1}}{2 \cdot 5}$

Step 5.1.2.2

Multiply $- 20$ by $- 1$ .

$x = \frac{- 1 \pm \sqrt{1 + 20}}{2 \cdot 5}$

Step 5.1.3

Add $1$ and $20$ .

$x = \frac{- 1 \pm \sqrt{21}}{2 \cdot 5}$

Step 5.2

Multiply $2$ by $5$ .

$x = \frac{- 1 \pm \sqrt{21}}{10}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{1 - \sqrt{21}}{10}, - \frac{1 + \sqrt{21}}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1 - \sqrt{21}}{10}, - \frac{1 + \sqrt{21}}{10}$

Decimal Form:

$x = 0.35825756 \dots, - 0.55825756 \dots$