Solve 1*8*10^-10=x(x+0.22)

$$1 \cdot 8 \times 10 ^ { - 10 } = x ( x + 0.22 )$$

Solve for x

$$x=\frac{\sqrt{30250002}}{50000}-0.11\approx 3.636363585 \cdot 10^{-9}$$

$$x=-\frac{\sqrt{30250002}}{50000}-0.11\approx -0.220000004$$

Steps Using the Quadratic Formula

Multiply 1 and 8 to get 8.

$$8\times 10^{-10}=x\left(x+0.22\right)$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$8\times \frac{1}{10000000000}=x\left(x+0.22\right)$$

Multiply 8 and \frac{1}{10000000000} to get \frac{1}{1250000000}.

$$\frac{1}{1250000000}=x\left(x+0.22\right)$$

Use the distributive property to multiply x by x+0.22.

$$\frac{1}{1250000000}=x^{2}+0.22x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+0.22x=\frac{1}{1250000000}$$

Subtract \frac{1}{1250000000} from both sides.

$$x^{2}+0.22x-\frac{1}{1250000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0.22 for b, and -\frac{1}{1250000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.22±\sqrt{0.22^{2}-4\left(-\frac{1}{1250000000}\right)}}{2}$$

Square 0.22 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0.22±\sqrt{0.0484-4\left(-\frac{1}{1250000000}\right)}}{2}$$

Multiply -4 times -\frac{1}{1250000000}.

$$x=\frac{-0.22±\sqrt{0.0484+\frac{1}{312500000}}}{2}$$

Add 0.0484 to \frac{1}{312500000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-0.22±\sqrt{\frac{15125001}{312500000}}}{2}$$

Take the square root of \frac{15125001}{312500000}.

$$x=\frac{-0.22±\frac{\sqrt{30250002}}{25000}}{2}$$

Now solve the equation x=\frac{-0.22±\frac{\sqrt{30250002}}{25000}}{2} when ± is plus. Add -0.22 to \frac{\sqrt{30250002}}{25000}.

$$x=\frac{\frac{\sqrt{30250002}}{25000}-\frac{11}{50}}{2}$$

Divide -\frac{11}{50}+\frac{\sqrt{30250002}}{25000} by 2.

$$x=\frac{\sqrt{30250002}}{50000}-\frac{11}{100}$$

Now solve the equation x=\frac{-0.22±\frac{\sqrt{30250002}}{25000}}{2} when ± is minus. Subtract \frac{\sqrt{30250002}}{25000} from -0.22.

$$x=\frac{-\frac{\sqrt{30250002}}{25000}-\frac{11}{50}}{2}$$

Divide -\frac{11}{50}-\frac{\sqrt{30250002}}{25000} by 2.

$$x=-\frac{\sqrt{30250002}}{50000}-\frac{11}{100}$$

The equation is now solved.

$$x=\frac{\sqrt{30250002}}{50000}-\frac{11}{100} x=-\frac{\sqrt{30250002}}{50000}-\frac{11}{100}$$

Steps for Completing the Square

Multiply 1 and 8 to get 8.

$$8\times 10^{-10}=x\left(x+0.22\right)$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$8\times \frac{1}{10000000000}=x\left(x+0.22\right)$$

Multiply 8 and \frac{1}{10000000000} to get \frac{1}{1250000000}.

$$\frac{1}{1250000000}=x\left(x+0.22\right)$$

Use the distributive property to multiply x by x+0.22.

$$\frac{1}{1250000000}=x^{2}+0.22x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+0.22x=\frac{1}{1250000000}$$

Divide 0.22, the coefficient of the x term, by 2 to get 0.11. Then add the square of 0.11 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0.22x+0.11^{2}=\frac{1}{1250000000}+0.11^{2}$$

Square 0.11 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0.22x+0.0121=\frac{1}{1250000000}+0.0121$$

Add \frac{1}{1250000000} to 0.0121 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+0.22x+0.0121=\frac{15125001}{1250000000}$$

Factor x^{2}+0.22x+0.0121. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.11\right)^{2}=\frac{15125001}{1250000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.11\right)^{2}}=\sqrt{\frac{15125001}{1250000000}}$$

Simplify.

$$x+0.11=\frac{\sqrt{30250002}}{50000} x+0.11=-\frac{\sqrt{30250002}}{50000}$$

Subtract 0.11 from both sides of the equation.

$$x=\frac{\sqrt{30250002}}{50000}-\frac{11}{100} x=-\frac{\sqrt{30250002}}{50000}-\frac{11}{100}$$