Calculus Examples

$x^{2} - 0.2 = - 0.06 x$

Step 1

Add $0.06 x$ to both sides of the equation.

$x^{2} - 0.2 + 0.06 x = 0$

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 $a = 1$ , $b = 0.06$ , and $c = - 0.2$ into the quadratic formula and solve for $x$ .

$\frac{- 0.06 \pm \sqrt{{0.06}^{2} - 4 \cdot (1 \cdot - 0.2)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $0.06$ to the power of $2$ .

$x = \frac{- 0.06 \pm \sqrt{0.0036 - 4 \cdot 1 \cdot - 0.2}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 0.2$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 0.06 \pm \sqrt{0.0036 - 4 \cdot - 0.2}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 0.2$ .

$x = \frac{- 0.06 \pm \sqrt{0.0036 + 0.8}}{2 \cdot 1}$

Step 4.1.3

Add $0.0036$ and $0.8$ .

$x = \frac{- 0.06 \pm \sqrt{0.8036}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 0.06 \pm \sqrt{0.8036}}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 0.41821869, - 0.47821869$