Finite Math Examples

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

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $4 x (6 x - 2)$ .

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Step 1.1.1.1

Simplify by multiplying through.

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Step 1.1.1.1.1

Apply the distributive property.

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

Step 1.1.1.1.2

Simplify the expression.

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Step 1.1.1.1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.1.1.1.2.2

Multiply $- 2$ by $4$ .

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

Step 1.1.1.2

Simplify each term.

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Step 1.1.1.2.1

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

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Step 1.1.1.2.1.1

Move $x$ .

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

Step 1.1.1.2.1.2

Multiply $x$ by $x$ .

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

Step 1.1.1.2.2

Multiply $4$ by $6$ .

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

Step 1.2

Subtract $64$ from both sides of the equation.

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

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 $a = 24$ , $b = - 8$ , and $c = - 64$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (24 \cdot - 64)}}{2 \cdot 24}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 24 \cdot - 64}}{2 \cdot 24}$

Step 4.1.2

Multiply $- 4 \cdot 24 \cdot - 64$ .

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Step 4.1.2.1

Multiply $- 4$ by $24$ .

$x = \frac{8 \pm \sqrt{64 - 96 \cdot - 64}}{2 \cdot 24}$

Step 4.1.2.2

Multiply $- 96$ by $- 64$ .

$x = \frac{8 \pm \sqrt{64 + 6144}}{2 \cdot 24}$

Step 4.1.3

Add $64$ and $6144$ .

$x = \frac{8 \pm \sqrt{6208}}{2 \cdot 24}$

Step 4.1.4

Rewrite $6208$ as $8^{2} \cdot 97$ .

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Step 4.1.4.1

Factor $64$ out of $6208$ .

$x = \frac{8 \pm \sqrt{64 (97)}}{2 \cdot 24}$

Step 4.1.4.2

Rewrite $64$ as $8^{2}$ .

$x = \frac{8 \pm \sqrt{8^{2} \cdot 97}}{2 \cdot 24}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{8 \pm 8 \sqrt{97}}{2 \cdot 24}$

Step 4.2

Multiply $2$ by $24$ .

$x = \frac{8 \pm 8 \sqrt{97}}{48}$

Step 4.3

Simplify $\frac{8 \pm 8 \sqrt{97}}{48}$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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