Finite Math Examples

$- 3 x (x - 4) = 2 x + 2$

Step 1

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

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 - 3 x (x - 4) = 2 x + 2$

Step 1.2

Simplify by adding zeros.

$- 3 x (x - 4) = 2 x + 2$

Step 1.3

Apply the distributive property.

$- 3 x \cdot x - 3 x \cdot - 4 = 2 x + 2$

Step 1.4

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.4.1

Move $x$ .

$- 3 (x \cdot x) - 3 x \cdot - 4 = 2 x + 2$

Step 1.4.2

Multiply $x$ by $x$ .

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

Step 1.5

Multiply $- 4$ by $- 3$ .

$- 3 x^{2} + 12 x = 2 x + 2$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $2 x$ from both sides of the equation.

$- 3 x^{2} + 12 x - 2 x = 2$

Step 2.2

Subtract $2 x$ from $12 x$ .

$- 3 x^{2} + 10 x = 2$

Step 3

Subtract $2$ from both sides of the equation.

$- 3 x^{2} + 10 x - 2 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = - 3$ , $b = 10$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (- 3 \cdot - 2)}}{2 \cdot - 3}$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Simplify the numerator.

Tap for more steps...

Step 6.1.1

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot - 3 \cdot - 2}}{2 \cdot - 3}$

Step 6.1.2

Multiply $- 4 \cdot - 3 \cdot - 2$ .

Tap for more steps...

Step 6.1.2.1

Multiply $- 4$ by $- 3$ .

$x = \frac{- 10 \pm \sqrt{100 + 12 \cdot - 2}}{2 \cdot - 3}$

Step 6.1.2.2

Multiply $12$ by $- 2$ .

$x = \frac{- 10 \pm \sqrt{100 - 24}}{2 \cdot - 3}$

Step 6.1.3

Subtract $24$ from $100$ .

$x = \frac{- 10 \pm \sqrt{76}}{2 \cdot - 3}$

Step 6.1.4

Rewrite $76$ as $2^{2} \cdot 19$ .

Tap for more steps...

Step 6.1.4.1

Factor $4$ out of $76$ .

$x = \frac{- 10 \pm \sqrt{4 (19)}}{2 \cdot - 3}$

Step 6.1.4.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 10 \pm \sqrt{2^{2} \cdot 19}}{2 \cdot - 3}$

Step 6.1.5

Pull terms out from under the radical.

$x = \frac{- 10 \pm 2 \sqrt{19}}{2 \cdot - 3}$

Step 6.2

Multiply $2$ by $- 3$ .

$x = \frac{- 10 \pm 2 \sqrt{19}}{- 6}$

Step 6.3

Simplify $\frac{- 10 \pm 2 \sqrt{19}}{- 6}$ .

$x = \frac{5 \pm \sqrt{19}}{3}$

Step 7

The final answer is the combination of both solutions.

$x = \frac{5 + \sqrt{19}}{3}, \frac{5 - \sqrt{19}}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 + \sqrt{19}}{3}, \frac{5 - \sqrt{19}}{3}$

Decimal Form:

$x = 3.11963298 \dots, 0.21370035 \dots$