Finite Math Examples

$4 x (6 x - 2) = 64$

Step 1

Subtract $64$ from both sides of the equation.

$4 x (6 x - 2) - 64 = 0$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$4 x (6 x) + 4 x \cdot - 2 - 64 = 0$

Step 2.2

Rewrite using the commutative property of multiplication.

$4 \cdot 6 x \cdot x + 4 x \cdot - 2 - 64 = 0$

Step 2.3

Multiply $- 2$ by $4$ .

$4 \cdot 6 x \cdot x - 8 x - 64 = 0$

Step 2.4

Simplify each term.

Tap for more steps...

Step 2.4.1

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

Tap for more steps...

Step 2.4.1.1

Move $x$ .

$4 \cdot 6 (x \cdot x) - 8 x - 64 = 0$

Step 2.4.1.2

Multiply $x$ by $x$ .

$4 \cdot 6 x^{2} - 8 x - 64 = 0$

Step 2.4.2

Multiply $4$ by $6$ .

$24 x^{2} - 8 x - 64 = 0$

Step 3

Factor $8$ out of $24 x^{2} - 8 x - 64$ .

Tap for more steps...

Step 3.1

Factor $8$ out of $24 x^{2}$ .

$8 (3 x^{2}) - 8 x - 64 = 0$

Step 3.2

Factor $8$ out of $- 8 x$ .

$8 (3 x^{2}) + 8 (- x) - 64 = 0$

Step 3.3

Factor $8$ out of $- 64$ .

$8 (3 x^{2}) + 8 (- x) + 8 (- 8) = 0$

Step 3.4

Factor $8$ out of $8 (3 x^{2}) + 8 (- x)$ .

$8 (3 x^{2} - x) + 8 (- 8) = 0$

Step 3.5

Factor $8$ out of $8 (3 x^{2} - x) + 8 (- 8)$ .

$8 (3 x^{2} - x - 8) = 0$

Step 4

Divide each term in $8 (3 x^{2} - x - 8) = 0$ by $8$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $8 (3 x^{2} - x - 8) = 0$ by $8$ .

$\frac{8 (3 x^{2} - x - 8)}{8} = \frac{0}{8}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{8 (3 x^{2} - x - 8)}{8} = \frac{0}{8}$

Step 4.2.1.2

Divide $3 x^{2} - x - 8$ by $1$ .

$3 x^{2} - x - 8 = \frac{0}{8}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $0$ by $8$ .

$3 x^{2} - x - 8 = 0$

Step 5

Use the quadratic formula to find the solutions.

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

Step 6

Substitute the values $a = 3$ , $b = - 1$ , and $c = - 8$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (3 \cdot - 8)}}{2 \cdot 3}$

Step 7

Simplify.

Tap for more steps...

Step 7.1

Simplify the numerator.

Tap for more steps...

Step 7.1.1

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

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 3 \cdot - 8}}{2 \cdot 3}$

Step 7.1.2

Multiply $- 4 \cdot 3 \cdot - 8$ .

Tap for more steps...

Step 7.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{1 \pm \sqrt{1 - 12 \cdot - 8}}{2 \cdot 3}$

Step 7.1.2.2

Multiply $- 12$ by $- 8$ .

$x = \frac{1 \pm \sqrt{1 + 96}}{2 \cdot 3}$

Step 7.1.3

Add $1$ and $96$ .

$x = \frac{1 \pm \sqrt{97}}{2 \cdot 3}$

Step 7.2

Multiply $2$ by $3$ .

$x = \frac{1 \pm \sqrt{97}}{6}$

Step 8

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

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

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 3 \cdot - 8}}{2 \cdot 3}$

Step 8.1.2

Multiply $- 4 \cdot 3 \cdot - 8$ .

Tap for more steps...

Step 8.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{1 \pm \sqrt{1 - 12 \cdot - 8}}{2 \cdot 3}$

Step 8.1.2.2

Multiply $- 12$ by $- 8$ .

$x = \frac{1 \pm \sqrt{1 + 96}}{2 \cdot 3}$

Step 8.1.3

Add $1$ and $96$ .

$x = \frac{1 \pm \sqrt{97}}{2 \cdot 3}$

Step 8.2

Multiply $2$ by $3$ .

$x = \frac{1 \pm \sqrt{97}}{6}$

Step 8.3

Change the $\pm$ to $+$ .

$x = \frac{1 + \sqrt{97}}{6}$

Step 9

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Tap for more steps...

Step 9.1

Simplify the numerator.

Tap for more steps...

Step 9.1.1

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

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 3 \cdot - 8}}{2 \cdot 3}$

Step 9.1.2

Multiply $- 4 \cdot 3 \cdot - 8$ .

Tap for more steps...

Step 9.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{1 \pm \sqrt{1 - 12 \cdot - 8}}{2 \cdot 3}$

Step 9.1.2.2

Multiply $- 12$ by $- 8$ .

$x = \frac{1 \pm \sqrt{1 + 96}}{2 \cdot 3}$

Step 9.1.3

Add $1$ and $96$ .

$x = \frac{1 \pm \sqrt{97}}{2 \cdot 3}$

Step 9.2

Multiply $2$ by $3$ .

$x = \frac{1 \pm \sqrt{97}}{6}$

Step 9.3

Change the $\pm$ to $-$ .

$x = \frac{1 - \sqrt{97}}{6}$

Step 10

The final answer is the combination of both solutions.

$x = \frac{1 + \sqrt{97}}{6}, \frac{1 - \sqrt{97}}{6}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 + \sqrt{97}}{6}, \frac{1 - \sqrt{97}}{6}$

Decimal Form:

$x = 1.80814296 \dots, - 1.47480963 \dots$