Solve 0.2x^2+0.1x^2-1=0

$$0.2 x ^ { 2 } + 0.1 x ^ { 2 } - 1 = 0$$

Solve for x

$$x = \frac{\sqrt{30}}{3} \approx 1.825741858$$

$$x = -\frac{\sqrt{30}}{3} \approx -1.825741858$$

Steps by Finding Square Root

Combine 0.2x^{2} and 0.1x^{2} to get 0.3x^{2}.

$$0.3x^{2}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$0.3x^{2}=1$$

Divide both sides by 0.3.

$$x^{2}=\frac{1}{0.3}$$

Expand \frac{1}{0.3} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{10}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{3} x=-\frac{\sqrt{30}}{3}$$

Steps Using the Quadratic Formula

Combine 0.2x^{2} and 0.1x^{2} to get 0.3x^{2}.

$$0.3x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.3 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.3\left(-1\right)}}{2\times 0.3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.3\left(-1\right)}}{2\times 0.3}$$

Multiply -4 times 0.3.

$$x=\frac{0±\sqrt{-1.2\left(-1\right)}}{2\times 0.3}$$

Multiply -1.2 times -1.

$$x=\frac{0±\sqrt{1.2}}{2\times 0.3}$$

Take the square root of 1.2.

$$x=\frac{0±\frac{\sqrt{30}}{5}}{2\times 0.3}$$

Multiply 2 times 0.3.

$$x=\frac{0±\frac{\sqrt{30}}{5}}{0.6}$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}}{5}}{0.6} when ± is plus.

$$x=\frac{\sqrt{30}}{3}$$

Now solve the equation x=\frac{0±\frac{\sqrt{30}}{5}}{0.6} when ± is minus.

$$x=-\frac{\sqrt{30}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{3} x=-\frac{\sqrt{30}}{3}$$