Solve (x+0.03)*x=3.7*10^-18

$$(x+0.03) \times x=3.7 \times { 10 }^{ -18 }$$

Solve for x

$$x=\frac{\sqrt{22500000000000370}}{10000000000}-0.015\approx 1.231653668 \cdot 10^{-16}$$

$$x=-\frac{\sqrt{22500000000000370}}{10000000000}-0.015\approx -0.03$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+0.03 by x.

$$x^{2}+0.03x=3.7\times 10^{-18}$$

Calculate 10 to the power of -18 and get \frac{1}{1000000000000000000}.

$$x^{2}+0.03x=3.7\times \frac{1}{1000000000000000000}$$

Multiply 3.7 and \frac{1}{1000000000000000000} to get \frac{37}{10000000000000000000}.

$$x^{2}+0.03x=\frac{37}{10000000000000000000}$$

Subtract \frac{37}{10000000000000000000} from both sides.

$$x^{2}+0.03x-\frac{37}{10000000000000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0.03 for b, and -\frac{37}{10000000000000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.03±\sqrt{0.03^{2}-4\left(-\frac{37}{10000000000000000000}\right)}}{2}$$

Square 0.03 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0.03±\sqrt{0.0009-4\left(-\frac{37}{10000000000000000000}\right)}}{2}$$

Multiply -4 times -\frac{37}{10000000000000000000}.

$$x=\frac{-0.03±\sqrt{0.0009+\frac{37}{2500000000000000000}}}{2}$$

Add 0.0009 to \frac{37}{2500000000000000000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-0.03±\sqrt{\frac{2250000000000037}{2500000000000000000}}}{2}$$

Take the square root of \frac{2250000000000037}{2500000000000000000}.

$$x=\frac{-0.03±\frac{\sqrt{22500000000000370}}{5000000000}}{2}$$

Now solve the equation x=\frac{-0.03±\frac{\sqrt{22500000000000370}}{5000000000}}{2} when ± is plus. Add -0.03 to \frac{\sqrt{22500000000000370}}{5000000000}.

$$x=\frac{\frac{\sqrt{22500000000000370}}{5000000000}-\frac{3}{100}}{2}$$

Divide -\frac{3}{100}+\frac{\sqrt{22500000000000370}}{5000000000} by 2.

$$x=\frac{\sqrt{22500000000000370}}{10000000000}-\frac{3}{200}$$

Now solve the equation x=\frac{-0.03±\frac{\sqrt{22500000000000370}}{5000000000}}{2} when ± is minus. Subtract \frac{\sqrt{22500000000000370}}{5000000000} from -0.03.

$$x=\frac{-\frac{\sqrt{22500000000000370}}{5000000000}-\frac{3}{100}}{2}$$

Divide -\frac{3}{100}-\frac{\sqrt{22500000000000370}}{5000000000} by 2.

$$x=-\frac{\sqrt{22500000000000370}}{10000000000}-\frac{3}{200}$$

The equation is now solved.

$$x=\frac{\sqrt{22500000000000370}}{10000000000}-\frac{3}{200} x=-\frac{\sqrt{22500000000000370}}{10000000000}-\frac{3}{200}$$

Steps for Completing the Square

Use the distributive property to multiply x+0.03 by x.

$$x^{2}+0.03x=3.7\times 10^{-18}$$

Calculate 10 to the power of -18 and get \frac{1}{1000000000000000000}.

$$x^{2}+0.03x=3.7\times \frac{1}{1000000000000000000}$$

Multiply 3.7 and \frac{1}{1000000000000000000} to get \frac{37}{10000000000000000000}.

$$x^{2}+0.03x=\frac{37}{10000000000000000000}$$

Divide 0.03, the coefficient of the x term, by 2 to get 0.015. Then add the square of 0.015 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0.03x+0.015^{2}=\frac{37}{10000000000000000000}+0.015^{2}$$

Square 0.015 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0.03x+0.000225=\frac{37}{10000000000000000000}+0.000225$$

Add \frac{37}{10000000000000000000} to 0.000225 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+0.03x+0.000225=\frac{2250000000000037}{10000000000000000000}$$

Factor x^{2}+0.03x+0.000225. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.015\right)^{2}=\frac{2250000000000037}{10000000000000000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.015\right)^{2}}=\sqrt{\frac{2250000000000037}{10000000000000000000}}$$

Simplify.

$$x+0.015=\frac{\sqrt{22500000000000370}}{10000000000} x+0.015=-\frac{\sqrt{22500000000000370}}{10000000000}$$

Subtract 0.015 from both sides of the equation.

$$x=\frac{\sqrt{22500000000000370}}{10000000000}-\frac{3}{200} x=-\frac{\sqrt{22500000000000370}}{10000000000}-\frac{3}{200}$$