Pre-Algebra Examples

$x^{2} - 0.8 = - 0.12 x$

Step 1

Add $0.12 x$ to both sides of the equation.

$x^{2} - 0.8 + 0.12 x = 0$

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 $a = 1$ , $b = 0.12$ , and $c = - 0.8$ into the quadratic formula and solve for $x$ .

$\frac{- 0.12 \pm \sqrt{{0.12}^{2} - 4 \cdot (1 \cdot - 0.8)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $0.12$ to the power of $2$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 - 4 \cdot 1 \cdot - 0.8}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 0.8$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 - 4 \cdot - 0.8}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 0.8$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 + 3.2}}{2 \cdot 1}$

Step 4.1.3

Add $0.0144$ and $3.2$ .

$x = \frac{- 0.12 \pm \sqrt{3.2144}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 0.12 \pm \sqrt{3.2144}}{2}$

Step 5

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

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $0.12$ to the power of $2$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 - 4 \cdot 1 \cdot - 0.8}}{2 \cdot 1}$

Step 5.1.2

Multiply $- 4 \cdot 1 \cdot - 0.8$ .

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Step 5.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 - 4 \cdot - 0.8}}{2 \cdot 1}$

Step 5.1.2.2

Multiply $- 4$ by $- 0.8$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 + 3.2}}{2 \cdot 1}$

Step 5.1.3

Add $0.0144$ and $3.2$ .

$x = \frac{- 0.12 \pm \sqrt{3.2144}}{2 \cdot 1}$

Step 5.2

Multiply $2$ by $1$ .

$x = \frac{- 0.12 \pm \sqrt{3.2144}}{2}$

Step 5.3

Change the $\pm$ to $+$ .

$x = \frac{- 0.12 + \sqrt{3.2144}}{2}$

Step 5.4

Add $- 0.12$ and $\sqrt{3.2144}$ .

$x = \frac{1.67287478}{2}$

Step 5.5

Divide $1.67287478$ by $2$ .

$x = 0.83643739$

Step 6

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

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $0.12$ to the power of $2$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 - 4 \cdot 1 \cdot - 0.8}}{2 \cdot 1}$

Step 6.1.2

Multiply $- 4 \cdot 1 \cdot - 0.8$ .

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Step 6.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 - 4 \cdot - 0.8}}{2 \cdot 1}$

Step 6.1.2.2

Multiply $- 4$ by $- 0.8$ .

$x = \frac{- 0.12 \pm \sqrt{0.0144 + 3.2}}{2 \cdot 1}$

Step 6.1.3

Add $0.0144$ and $3.2$ .

$x = \frac{- 0.12 \pm \sqrt{3.2144}}{2 \cdot 1}$

Step 6.2

Multiply $2$ by $1$ .

$x = \frac{- 0.12 \pm \sqrt{3.2144}}{2}$

Step 6.3

Change the $\pm$ to $-$ .

$x = \frac{- 0.12 - \sqrt{3.2144}}{2}$

Step 6.4

Subtract $\sqrt{3.2144}$ from $- 0.12$ .

$x = \frac{- 1.91287478}{2}$

Step 6.5

Divide $- 1.91287478$ by $2$ .

$x = - 0.95643739$

Step 7

The final answer is the combination of both solutions.

$x = 0.83643739, - 0.95643739$