Algebra Examples

$4 x (x - 3) = 24$

Step 1

Divide each term in $4 x (x - 3) = 24$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 x (x - 3) = 24$ by $4$ .

$\frac{4 x (x - 3)}{4} = \frac{24}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 x (x - 3)}{4} = \frac{24}{4}$

Step 1.2.1.2

Divide $x (x - 3)$ by $1$ .

$x (x - 3) = \frac{24}{4}$

Step 1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 = \frac{24}{4}$

Step 1.2.3

Simplify the expression.

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Step 1.2.3.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 = \frac{24}{4}$

Step 1.2.3.2

Move $- 3$ to the left of $x$ .

$x^{2} - 3 x = \frac{24}{4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $24$ by $4$ .

$x^{2} - 3 x = 6$

Step 2

Subtract $6$ from both sides of the equation.

$x^{2} - 3 x - 6 = 0$

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 $a = 1$ , $b = - 3$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (1 \cdot - 6)}}{2 \cdot 1}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 6}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot - 6$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot - 6}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $- 6$ .

$x = \frac{3 \pm \sqrt{9 + 24}}{2 \cdot 1}$

Step 5.1.3

Add $9$ and $24$ .

$x = \frac{3 \pm \sqrt{33}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{3 \pm \sqrt{33}}{2}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{3 + \sqrt{33}}{2}, \frac{3 - \sqrt{33}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 + \sqrt{33}}{2}, \frac{3 - \sqrt{33}}{2}$

Decimal Form:

$x = 4.37228132 \dots, - 1.37228132 \dots$