Algebra Examples

$x \cdot 0.6 (x - 1) = 9 (x + 2)$

Step 1

Simplify $x \cdot (0.6 (x - 1))$ .

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Step 1.1

Rewrite.

$0 + 0 + x \cdot (0.6 (x - 1)) = 9 (x + 2)$

Step 1.2

Rewrite using the commutative property of multiplication.

$0.6 x (x - 1) = 9 (x + 2)$

Step 1.3

Apply the distributive property.

$0.6 x \cdot x + 0.6 x \cdot - 1 = 9 (x + 2)$

Step 1.4

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

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Step 1.4.1

Move $x$ .

$0.6 (x \cdot x) + 0.6 x \cdot - 1 = 9 (x + 2)$

Step 1.4.2

Multiply $x$ by $x$ .

$0.6 x^{2} + 0.6 x \cdot - 1 = 9 (x + 2)$

Step 1.5

Multiply $- 1$ by $0.6$ .

$0.6 x^{2} - 0.6 x = 9 (x + 2)$

Step 2

Simplify $9 (x + 2)$ .

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Step 2.1

Apply the distributive property.

$0.6 x^{2} - 0.6 x = 9 x + 9 \cdot 2$

Step 2.2

Multiply $9$ by $2$ .

$0.6 x^{2} - 0.6 x = 9 x + 18$

Step 3

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

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Step 3.1

Subtract $9 x$ from both sides of the equation.

$0.6 x^{2} - 0.6 x - 9 x = 18$

Step 3.2

Subtract $9 x$ from $- 0.6 x$ .

$0.6 x^{2} - 9.6 x = 18$

Step 4

Subtract $18$ from both sides of the equation.

$0.6 x^{2} - 9.6 x - 18 = 0$

Step 5

Factor $0.6$ out of $0.6 x^{2} - 9.6 x - 18$ .

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Step 5.1

Factor $0.6$ out of $0.6 x^{2}$ .

$0.6 (x^{2}) - 9.6 x - 18 = 0$

Step 5.2

Factor $0.6$ out of $- 9.6 x$ .

$0.6 (x^{2}) + 0.6 (- 16 x) - 18 = 0$

Step 5.3

Factor $0.6$ out of $- 18$ .

$0.6 x^{2} + 0.6 (- 16 x) + 0.6 \cdot - 30 = 0$

Step 5.4

Factor $0.6$ out of $0.6 x^{2} + 0.6 (- 16 x)$ .

$0.6 (x^{2} - 16 x) + 0.6 \cdot - 30 = 0$

Step 5.5

Factor $0.6$ out of $0.6 (x^{2} - 16 x) + 0.6 \cdot - 30$ .

$0.6 (x^{2} - 16 x - 30) = 0$

Step 6

Divide each term in $0.6 (x^{2} - 16 x - 30) = 0$ by $0.6$ and simplify.

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Step 6.1

Divide each term in $0.6 (x^{2} - 16 x - 30) = 0$ by $0.6$ .

$\frac{0.6 (x^{2} - 16 x - 30)}{0.6} = \frac{0}{0.6}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $0.6$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{0.6 (x^{2} - 16 x - 30)}{0.6} = \frac{0}{0.6}$

Step 6.2.1.2

Divide $x^{2} - 16 x - 30$ by $1$ .

$x^{2} - 16 x - 30 = \frac{0}{0.6}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $0$ by $0.6$ .

$x^{2} - 16 x - 30 = 0$

Step 7

Use the quadratic formula to find the solutions.

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

Step 8

Substitute the values $a = 1$ , $b = - 16$ , and $c = - 30$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (1 \cdot - 30)}}{2 \cdot 1}$

Step 9

Simplify.

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Step 9.1

Simplify the numerator.

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Step 9.1.1

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 1 \cdot - 30}}{2 \cdot 1}$

Step 9.1.2

Multiply $- 4 \cdot 1 \cdot - 30$ .

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Step 9.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot - 30}}{2 \cdot 1}$

Step 9.1.2.2

Multiply $- 4$ by $- 30$ .

$x = \frac{16 \pm \sqrt{256 + 120}}{2 \cdot 1}$

Step 9.1.3

Add $256$ and $120$ .

$x = \frac{16 \pm \sqrt{376}}{2 \cdot 1}$

Step 9.1.4

Rewrite $376$ as $2^{2} \cdot 94$ .

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Step 9.1.4.1

Factor $4$ out of $376$ .

$x = \frac{16 \pm \sqrt{4 (94)}}{2 \cdot 1}$

Step 9.1.4.2

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

$x = \frac{16 \pm \sqrt{2^{2} \cdot 94}}{2 \cdot 1}$

Step 9.1.5

Pull terms out from under the radical.

$x = \frac{16 \pm 2 \sqrt{94}}{2 \cdot 1}$

Step 9.2

Multiply $2$ by $1$ .

$x = \frac{16 \pm 2 \sqrt{94}}{2}$

Step 9.3

Simplify $\frac{16 \pm 2 \sqrt{94}}{2}$ .

$x = 8 \pm \sqrt{94}$

Step 10

The final answer is the combination of both solutions.

$x = 8 + \sqrt{94}, 8 - \sqrt{94}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$x = 8 + \sqrt{94}, 8 - \sqrt{94}$

Decimal Form:

$x = 17.69535971 \dots, - 1.69535971 \dots$