Algebra Examples

$0.2 x^{2} + 1.2 = 3.4$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Subtract $3.4$ from both sides of the equation.

$0.2 x^{2} + 1.2 - 3.4 = 0$

Step 1.2

Subtract $3.4$ from $1.2$ .

$0.2 x^{2} - 2.2 = 0$

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 $a = 0.2$ , $b = 0$ , and $c = - 2.2$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (0.2 \cdot - 2.2)}}{2 \cdot 0.2}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 0.2 \cdot - 2.2}}{2 \cdot 0.2}$

Step 4.1.2

Multiply $- 4 \cdot 0.2 \cdot - 2.2$ .

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Step 4.1.2.1

Multiply $- 4$ by $0.2$ .

$x = \frac{0 \pm \sqrt{0 - 0.8 \cdot - 2.2}}{2 \cdot 0.2}$

Step 4.1.2.2

Multiply $- 0.8$ by $- 2.2$ .

$x = \frac{0 \pm \sqrt{0 + 1.76}}{2 \cdot 0.2}$

Step 4.1.3

Add $0$ and $1.76$ .

$x = \frac{0 \pm \sqrt{1.76}}{2 \cdot 0.2}$

Step 4.2

Multiply $2$ by $0.2$ .

$x = \frac{0 \pm \sqrt{1.76}}{0.4}$

Step 4.3

Multiply by $1$ .

$x = \frac{1 (0 \pm \sqrt{1.76})}{0.4}$

Step 4.4

Factor $0.4$ out of $0.4$ .

$x = \frac{1 (0 \pm \sqrt{1.76})}{0.4 (1)}$

Step 4.5

Separate fractions.

$x = \frac{1}{0.4} \cdot \frac{0 \pm \sqrt{1.76}}{1}$

Step 4.6

Divide $1$ by $0.4$ .

$x = 2.5 (\frac{0 \pm \sqrt{1.76}}{1})$

Step 4.7

Divide $0 \pm \sqrt{1.76}$ by $1$ .

$x = 2.5 (0 \pm \sqrt{1.76})$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 2.5 (0 \pm \sqrt{1.76})$

Decimal Form:

$x = 3.31662479 \dots, - 3.31662479 \dots$