Solve x^2+0.04x=0.045*(1/3+4.9)

$${ x }^{ 2 } +0.04x=0.045 \times ( \frac{ 1 }{ 3 } +4.9)$$

Solve for x

$$x=\frac{\sqrt{2359}}{100}-0.02\approx 0.465695378$$

$$x=-\frac{\sqrt{2359}}{100}-0.02\approx -0.505695378$$

Steps Using the Quadratic Formula

Add \frac{1}{3} and 4.9 to get \frac{157}{30}.

$$x^{2}+0.04x=0.045\times \frac{157}{30}$$

Multiply 0.045 and \frac{157}{30} to get \frac{471}{2000}.

$$x^{2}+0.04x=\frac{471}{2000}$$

Subtract \frac{471}{2000} from both sides.

$$x^{2}+0.04x-\frac{471}{2000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0.04 for b, and -\frac{471}{2000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-0.04±\sqrt{0.04^{2}-4\left(-\frac{471}{2000}\right)}}{2}$$

Square 0.04 by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-0.04±\sqrt{0.0016-4\left(-\frac{471}{2000}\right)}}{2}$$

Multiply -4 times -\frac{471}{2000}.

$$x=\frac{-0.04±\sqrt{0.0016+\frac{471}{500}}}{2}$$

Add 0.0016 to \frac{471}{500} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-0.04±\sqrt{\frac{2359}{2500}}}{2}$$

Take the square root of \frac{2359}{2500}.

$$x=\frac{-0.04±\frac{\sqrt{2359}}{50}}{2}$$

Now solve the equation x=\frac{-0.04±\frac{\sqrt{2359}}{50}}{2} when ± is plus. Add -0.04 to \frac{\sqrt{2359}}{50}.

$$x=\frac{\frac{\sqrt{2359}}{50}-\frac{1}{25}}{2}$$

Divide -\frac{1}{25}+\frac{\sqrt{2359}}{50} by 2.

$$x=\frac{\sqrt{2359}}{100}-\frac{1}{50}$$

Now solve the equation x=\frac{-0.04±\frac{\sqrt{2359}}{50}}{2} when ± is minus. Subtract \frac{\sqrt{2359}}{50} from -0.04.

$$x=\frac{-\frac{\sqrt{2359}}{50}-\frac{1}{25}}{2}$$

Divide -\frac{1}{25}-\frac{\sqrt{2359}}{50} by 2.

$$x=-\frac{\sqrt{2359}}{100}-\frac{1}{50}$$

The equation is now solved.

$$x=\frac{\sqrt{2359}}{100}-\frac{1}{50} x=-\frac{\sqrt{2359}}{100}-\frac{1}{50}$$

Steps for Completing the Square

Add \frac{1}{3} and 4.9 to get \frac{157}{30}.

$$x^{2}+0.04x=0.045\times \frac{157}{30}$$

Multiply 0.045 and \frac{157}{30} to get \frac{471}{2000}.

$$x^{2}+0.04x=\frac{471}{2000}$$

Divide 0.04, the coefficient of the x term, by 2 to get 0.02. Then add the square of 0.02 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+0.04x+0.02^{2}=\frac{471}{2000}+0.02^{2}$$

Square 0.02 by squaring both the numerator and the denominator of the fraction.

$$x^{2}+0.04x+0.0004=\frac{471}{2000}+0.0004$$

Add \frac{471}{2000} to 0.0004 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+0.04x+0.0004=\frac{2359}{10000}$$

Factor x^{2}+0.04x+0.0004. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+0.02\right)^{2}=\frac{2359}{10000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+0.02\right)^{2}}=\sqrt{\frac{2359}{10000}}$$

Simplify.

$$x+0.02=\frac{\sqrt{2359}}{100} x+0.02=-\frac{\sqrt{2359}}{100}$$

Subtract 0.02 from both sides of the equation.

$$x=\frac{\sqrt{2359}}{100}-\frac{1}{50} x=-\frac{\sqrt{2359}}{100}-\frac{1}{50}$$