Solve x^2+0,3x=1,9*10^-7

$$x ^ { 2 } + 0,3 x = 1,9 \cdot 10 ^ { - 7 }$$

Solve for x

$$x=\frac{\sqrt{2250019}}{10000}-0,15\approx 0.000000633$$

$$x=-\frac{\sqrt{2250019}}{10000}-0,15\approx -0.300000633$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$x^{2}+0,3x=1,9\times \frac{1}{10000000}$$

Multiply 1,9 and \frac{1}{10000000} to get \frac{19}{100000000}.

$$x^{2}+0,3x=\frac{19}{100000000}$$

Subtract \frac{19}{100000000} from both sides.

$$x^{2}+0,3x-\frac{19}{100000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0,3 for b, and -\frac{19}{100000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0,3±\sqrt{0,3^{2}-4\left(-\frac{19}{100000000}\right)}}{2}$$

Square 0,3 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0,3±\sqrt{0,09-4\left(-\frac{19}{100000000}\right)}}{2}$$

Multiply -4 times -\frac{19}{100000000}.

$$x=\frac{-0,3±\sqrt{0,09+\frac{19}{25000000}}}{2}$$

Add 0,09 to \frac{19}{25000000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-0,3±\sqrt{\frac{2250019}{25000000}}}{2}$$

Take the square root of \frac{2250019}{25000000}.

$$x=\frac{-0,3±\frac{\sqrt{2250019}}{5000}}{2}$$

Now solve the equation x=\frac{-0,3±\frac{\sqrt{2250019}}{5000}}{2} when ± is plus. Add -0,3 to \frac{\sqrt{2250019}}{5000}.

$$x=\frac{\frac{\sqrt{2250019}}{5000}-\frac{3}{10}}{2}$$

Divide -\frac{3}{10}+\frac{\sqrt{2250019}}{5000} by 2.

$$x=\frac{\sqrt{2250019}}{10000}-\frac{3}{20}$$

Now solve the equation x=\frac{-0,3±\frac{\sqrt{2250019}}{5000}}{2} when ± is minus. Subtract \frac{\sqrt{2250019}}{5000} from -0,3.

$$x=\frac{-\frac{\sqrt{2250019}}{5000}-\frac{3}{10}}{2}$$

Divide -\frac{3}{10}-\frac{\sqrt{2250019}}{5000} by 2.

$$x=-\frac{\sqrt{2250019}}{10000}-\frac{3}{20}$$

The equation is now solved.

$$x=\frac{\sqrt{2250019}}{10000}-\frac{3}{20} x=-\frac{\sqrt{2250019}}{10000}-\frac{3}{20}$$

Steps for Completing the Square

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$x^{2}+0,3x=1,9\times \frac{1}{10000000}$$

Multiply 1,9 and \frac{1}{10000000} to get \frac{19}{100000000}.

$$x^{2}+0,3x=\frac{19}{100000000}$$

Divide 0,3, the coefficient of the x term, by 2 to get 0,15. Then add the square of 0,15 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0,3x+0,15^{2}=\frac{19}{100000000}+0,15^{2}$$

Square 0,15 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0,3x+0,0225=\frac{19}{100000000}+0,0225$$

Add \frac{19}{100000000} to 0,0225 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+0,3x+0,0225=\frac{2250019}{100000000}$$

Factor x^{2}+0,3x+0,0225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0,15\right)^{2}=\frac{2250019}{100000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0,15\right)^{2}}=\sqrt{\frac{2250019}{100000000}}$$

Simplify.

$$x+0,15=\frac{\sqrt{2250019}}{10000} x+0,15=-\frac{\sqrt{2250019}}{10000}$$

Subtract 0,15 from both sides of the equation.

$$x=\frac{\sqrt{2250019}}{10000}-\frac{3}{20} x=-\frac{\sqrt{2250019}}{10000}-\frac{3}{20}$$