Pre-Algebra Examples

$1.2 x^{2} = 2.1 x + 1.7$

Step 1

Subtract $2.1 x$ from both sides of the equation.

$1.2 x^{2} - 2.1 x = 1.7$

Step 2

Subtract $1.7$ from both sides of the equation.

$1.2 x^{2} - 2.1 x - 1.7 = 0$

Step 3

Factor $0.1$ out of $1.2 x^{2} - 2.1 x - 1.7$ .

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Step 3.1

Factor $0.1$ out of $1.2 x^{2}$ .

$0.1 (12 x^{2}) - 2.1 x - 1.7 = 0$

Step 3.2

Factor $0.1$ out of $- 2.1 x$ .

$0.1 (12 x^{2}) + 0.1 (- 21 x) - 1.7 = 0$

Step 3.3

Factor $0.1$ out of $- 1.7$ .

$0.1 (12 x^{2}) + 0.1 (- 21 x) + 0.1 (- 17) = 0$

Step 3.4

Factor $0.1$ out of $0.1 (12 x^{2}) + 0.1 (- 21 x)$ .

$0.1 (12 x^{2} - 21 x) + 0.1 (- 17) = 0$

Step 3.5

Factor $0.1$ out of $0.1 (12 x^{2} - 21 x) + 0.1 (- 17)$ .

$0.1 (12 x^{2} - 21 x - 17) = 0$

Step 4

Divide each term in $0.1 (12 x^{2} - 21 x - 17) = 0$ by $0.1$ and simplify.

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Step 4.1

Divide each term in $0.1 (12 x^{2} - 21 x - 17) = 0$ by $0.1$ .

$\frac{0.1 (12 x^{2} - 21 x - 17)}{0.1} = \frac{0}{0.1}$

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.

$\frac{0.1 (12 x^{2} - 21 x - 17)}{0.1} = \frac{0}{0.1}$

Step 4.2.1.2

Divide $12 x^{2} - 21 x - 17$ by $1$ .

$12 x^{2} - 21 x - 17 = \frac{0}{0.1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $0.1$ .

$12 x^{2} - 21 x - 17 = 0$

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 $a = 12$ , $b = - 21$ , and $c = - 17$ into the quadratic formula and solve for $x$ .

$\frac{21 \pm \sqrt{{(- 21)}^{2} - 4 \cdot (12 \cdot - 17)}}{2 \cdot 12}$

Step 7

Simplify.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $- 21$ to the power of $2$ .

$x = \frac{21 \pm \sqrt{441 - 4 \cdot 12 \cdot - 17}}{2 \cdot 12}$

Step 7.1.2

Multiply $- 4 \cdot 12 \cdot - 17$ .

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Step 7.1.2.1

Multiply $- 4$ by $12$ .

$x = \frac{21 \pm \sqrt{441 - 48 \cdot - 17}}{2 \cdot 12}$

Step 7.1.2.2

Multiply $- 48$ by $- 17$ .

$x = \frac{21 \pm \sqrt{441 + 816}}{2 \cdot 12}$

Step 7.1.3

Add $441$ and $816$ .

$x = \frac{21 \pm \sqrt{1257}}{2 \cdot 12}$

Step 7.2

Multiply $2$ by $12$ .

$x = \frac{21 \pm \sqrt{1257}}{24}$

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 $- 21$ to the power of $2$ .

$x = \frac{21 \pm \sqrt{441 - 4 \cdot 12 \cdot - 17}}{2 \cdot 12}$

Step 8.1.2

Multiply $- 4 \cdot 12 \cdot - 17$ .

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Step 8.1.2.1

Multiply $- 4$ by $12$ .

$x = \frac{21 \pm \sqrt{441 - 48 \cdot - 17}}{2 \cdot 12}$

Step 8.1.2.2

Multiply $- 48$ by $- 17$ .

$x = \frac{21 \pm \sqrt{441 + 816}}{2 \cdot 12}$

Step 8.1.3

Add $441$ and $816$ .

$x = \frac{21 \pm \sqrt{1257}}{2 \cdot 12}$

Step 8.2

Multiply $2$ by $12$ .

$x = \frac{21 \pm \sqrt{1257}}{24}$

Step 8.3

Change the $\pm$ to $+$ .

$x = \frac{21 + \sqrt{1257}}{24}$

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 $- 21$ to the power of $2$ .

$x = \frac{21 \pm \sqrt{441 - 4 \cdot 12 \cdot - 17}}{2 \cdot 12}$

Step 9.1.2

Multiply $- 4 \cdot 12 \cdot - 17$ .

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Step 9.1.2.1

Multiply $- 4$ by $12$ .

$x = \frac{21 \pm \sqrt{441 - 48 \cdot - 17}}{2 \cdot 12}$

Step 9.1.2.2

Multiply $- 48$ by $- 17$ .

$x = \frac{21 \pm \sqrt{441 + 816}}{2 \cdot 12}$

Step 9.1.3

Add $441$ and $816$ .

$x = \frac{21 \pm \sqrt{1257}}{2 \cdot 12}$

Step 9.2

Multiply $2$ by $12$ .

$x = \frac{21 \pm \sqrt{1257}}{24}$

Step 9.3

Change the $\pm$ to $-$ .

$x = \frac{21 - \sqrt{1257}}{24}$

Step 10

The final answer is the combination of both solutions.

$x = \frac{21 + \sqrt{1257}}{24}, \frac{21 - \sqrt{1257}}{24}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$x = \frac{21 + \sqrt{1257}}{24}, \frac{21 - \sqrt{1257}}{24}$

Decimal Form:

$x = 2.35225815 \dots, - 0.60225815 \dots$