Pre-Algebra Examples

$- 0.3 x (0.7 x - 0.9) = - 1.83$

Step 1

Divide each term in $- 0.3 x (0.7 x - 0.9) = - 1.83$ by $- 0.3$ and simplify.

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Step 1.1

Divide each term in $- 0.3 x (0.7 x - 0.9) = - 1.83$ by $- 0.3$ .

$\frac{- 0.3 x (0.7 x - 0.9)}{- 0.3} = \frac{- 1.83}{- 0.3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify terms.

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Step 1.2.1.1

Cancel the common factor of $- 0.3$ .

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Step 1.2.1.1.1

Cancel the common factor.

$\frac{- 0.3 x (0.7 x - 0.9)}{- 0.3} = \frac{- 1.83}{- 0.3}$

Step 1.2.1.1.2

Divide $x (0.7 x - 0.9)$ by $1$ .

$x (0.7 x - 0.9) = \frac{- 1.83}{- 0.3}$

Step 1.2.1.2

Apply the distributive property.

$x (0.7 x) + x \cdot - 0.9 = \frac{- 1.83}{- 0.3}$

Step 1.2.1.3

Reorder.

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Step 1.2.1.3.1

Rewrite using the commutative property of multiplication.

$0.7 x \cdot x + x \cdot - 0.9 = \frac{- 1.83}{- 0.3}$

Step 1.2.1.3.2

Move $- 0.9$ to the left of $x$ .

$0.7 x \cdot x - 0.9 \cdot x = \frac{- 1.83}{- 0.3}$

Step 1.2.2

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

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Step 1.2.2.1

Move $x$ .

$0.7 (x \cdot x) - 0.9 \cdot x = \frac{- 1.83}{- 0.3}$

Step 1.2.2.2

Multiply $x$ by $x$ .

$0.7 x^{2} - 0.9 \cdot x = \frac{- 1.83}{- 0.3}$

$0.7 x^{2} - 0.9 x = \frac{- 1.83}{- 0.3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $- 1.83$ by $- 0.3$ .

$0.7 x^{2} - 0.9 x = 6.1$

Step 2

Subtract $6.1$ from both sides of the equation.

$0.7 x^{2} - 0.9 x - 6.1 = 0$

Step 3

Factor $0.1$ out of $0.7 x^{2} - 0.9 x - 6.1$ .

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Step 3.1

Factor $0.1$ out of $0.7 x^{2}$ .

$0.1 (7 x^{2}) - 0.9 x - 6.1 = 0$

Step 3.2

Factor $0.1$ out of $- 0.9 x$ .

$0.1 (7 x^{2}) + 0.1 (- 9 x) - 6.1 = 0$

Step 3.3

Factor $0.1$ out of $- 6.1$ .

$0.1 (7 x^{2}) + 0.1 (- 9 x) + 0.1 (- 61) = 0$

Step 3.4

Factor $0.1$ out of $0.1 (7 x^{2}) + 0.1 (- 9 x)$ .

$0.1 (7 x^{2} - 9 x) + 0.1 (- 61) = 0$

Step 3.5

Factor $0.1$ out of $0.1 (7 x^{2} - 9 x) + 0.1 (- 61)$ .

$0.1 (7 x^{2} - 9 x - 61) = 0$

Step 4

Divide each term in $0.1 (7 x^{2} - 9 x - 61) = 0$ by $0.1$ and simplify.

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Step 4.1

Divide each term in $0.1 (7 x^{2} - 9 x - 61) = 0$ by $0.1$ .

$\frac{0.1 (7 x^{2} - 9 x - 61)}{0.1} = \frac{0}{0.1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.1 (7 x^{2} - 9 x - 61)}{0.1} = \frac{0}{0.1}$

Step 4.2.1.2

Divide $7 x^{2} - 9 x - 61$ by $1$ .

$7 x^{2} - 9 x - 61 = \frac{0}{0.1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $0.1$ .

$7 x^{2} - 9 x - 61 = 0$

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 $a = 7$ , $b = - 9$ , and $c = - 61$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (7 \cdot - 61)}}{2 \cdot 7}$

Step 7

Simplify.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 7 \cdot - 61}}{2 \cdot 7}$

Step 7.1.2

Multiply $- 4 \cdot 7 \cdot - 61$ .

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Step 7.1.2.1

Multiply $- 4$ by $7$ .

$x = \frac{9 \pm \sqrt{81 - 28 \cdot - 61}}{2 \cdot 7}$

Step 7.1.2.2

Multiply $- 28$ by $- 61$ .

$x = \frac{9 \pm \sqrt{81 + 1708}}{2 \cdot 7}$

Step 7.1.3

Add $81$ and $1708$ .

$x = \frac{9 \pm \sqrt{1789}}{2 \cdot 7}$

Step 7.2

Multiply $2$ by $7$ .

$x = \frac{9 \pm \sqrt{1789}}{14}$

Step 8

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

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Step 8.1

Simplify the numerator.

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Step 8.1.1

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 7 \cdot - 61}}{2 \cdot 7}$

Step 8.1.2

Multiply $- 4 \cdot 7 \cdot - 61$ .

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Step 8.1.2.1

Multiply $- 4$ by $7$ .

$x = \frac{9 \pm \sqrt{81 - 28 \cdot - 61}}{2 \cdot 7}$

Step 8.1.2.2

Multiply $- 28$ by $- 61$ .

$x = \frac{9 \pm \sqrt{81 + 1708}}{2 \cdot 7}$

Step 8.1.3

Add $81$ and $1708$ .

$x = \frac{9 \pm \sqrt{1789}}{2 \cdot 7}$

Step 8.2

Multiply $2$ by $7$ .

$x = \frac{9 \pm \sqrt{1789}}{14}$

Step 8.3

Change the $\pm$ to $+$ .

$x = \frac{9 + \sqrt{1789}}{14}$

Step 9

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

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Step 9.1

Simplify the numerator.

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Step 9.1.1

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 7 \cdot - 61}}{2 \cdot 7}$

Step 9.1.2

Multiply $- 4 \cdot 7 \cdot - 61$ .

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Step 9.1.2.1

Multiply $- 4$ by $7$ .

$x = \frac{9 \pm \sqrt{81 - 28 \cdot - 61}}{2 \cdot 7}$

Step 9.1.2.2

Multiply $- 28$ by $- 61$ .

$x = \frac{9 \pm \sqrt{81 + 1708}}{2 \cdot 7}$

Step 9.1.3

Add $81$ and $1708$ .

$x = \frac{9 \pm \sqrt{1789}}{2 \cdot 7}$

Step 9.2

Multiply $2$ by $7$ .

$x = \frac{9 \pm \sqrt{1789}}{14}$

Step 9.3

Change the $\pm$ to $-$ .

$x = \frac{9 - \sqrt{1789}}{14}$

Step 10

The final answer is the combination of both solutions.

$x = \frac{9 + \sqrt{1789}}{14}, \frac{9 - \sqrt{1789}}{14}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9 + \sqrt{1789}}{14}, \frac{9 - \sqrt{1789}}{14}$

Decimal Form:

$x = 3.66404085 \dots, - 2.37832656 \dots$