Solve left(2xright)^2/200-x=9.59*10^-3

$$\frac{ { \left(2x \right) }^{ 2 } }{ 200-x } =9.59 \times { 10 }^{ -3 }$$

Solve for x

$$x=\frac{\sqrt{306880919681}-959}{800000}\approx 0.691261673$$

$$x=\frac{-\sqrt{306880919681}-959}{800000}\approx -0.693659173$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 200 since division by zero is not defined. Multiply both sides of the equation by -x+200.

$$\left(2x\right)^{2}=9.59\times 10^{-3}\left(-x+200\right)$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}=9.59\times 10^{-3}\left(-x+200\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=9.59\times 10^{-3}\left(-x+200\right)$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$4x^{2}=9.59\times \frac{1}{1000}\left(-x+200\right)$$

Multiply 9.59 and \frac{1}{1000} to get \frac{959}{100000}.

$$4x^{2}=\frac{959}{100000}\left(-x+200\right)$$

Use the distributive property to multiply \frac{959}{100000} by -x+200.

$$4x^{2}=-\frac{959}{100000}x+\frac{959}{500}$$

Add \frac{959}{100000}x to both sides.

$$4x^{2}+\frac{959}{100000}x=\frac{959}{500}$$

Subtract \frac{959}{500} from both sides.

$$4x^{2}+\frac{959}{100000}x-\frac{959}{500}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, \frac{959}{100000} for b, and -\frac{959}{500} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{959}{100000}±\sqrt{\left(\frac{959}{100000}\right)^{2}-4\times 4\left(-\frac{959}{500}\right)}}{2\times 4}$$

Square \frac{959}{100000} by squaring both the numerator and the denominator of the fraction.

$$x=\frac{-\frac{959}{100000}±\sqrt{\frac{919681}{10000000000}-4\times 4\left(-\frac{959}{500}\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{-\frac{959}{100000}±\sqrt{\frac{919681}{10000000000}-16\left(-\frac{959}{500}\right)}}{2\times 4}$$

Multiply -16 times -\frac{959}{500}.

$$x=\frac{-\frac{959}{100000}±\sqrt{\frac{919681}{10000000000}+\frac{3836}{125}}}{2\times 4}$$

Add \frac{919681}{10000000000} to \frac{3836}{125} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{-\frac{959}{100000}±\sqrt{\frac{306880919681}{10000000000}}}{2\times 4}$$

Take the square root of \frac{306880919681}{10000000000}.

$$x=\frac{-\frac{959}{100000}±\frac{\sqrt{306880919681}}{100000}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-\frac{959}{100000}±\frac{\sqrt{306880919681}}{100000}}{8}$$

Now solve the equation x=\frac{-\frac{959}{100000}±\frac{\sqrt{306880919681}}{100000}}{8} when ± is plus. Add -\frac{959}{100000} to \frac{\sqrt{306880919681}}{100000}.

$$x=\frac{\sqrt{306880919681}-959}{8\times 100000}$$

Divide \frac{-959+\sqrt{306880919681}}{100000} by 8.

$$x=\frac{\sqrt{306880919681}-959}{800000}$$

Now solve the equation x=\frac{-\frac{959}{100000}±\frac{\sqrt{306880919681}}{100000}}{8} when ± is minus. Subtract \frac{\sqrt{306880919681}}{100000} from -\frac{959}{100000}.

$$x=\frac{-\sqrt{306880919681}-959}{8\times 100000}$$

Divide \frac{-959-\sqrt{306880919681}}{100000} by 8.

$$x=\frac{-\sqrt{306880919681}-959}{800000}$$

The equation is now solved.

$$x=\frac{\sqrt{306880919681}-959}{800000} x=\frac{-\sqrt{306880919681}-959}{800000}$$

Steps for Completing the Square

Variable x cannot be equal to 200 since division by zero is not defined. Multiply both sides of the equation by -x+200.

$$\left(2x\right)^{2}=9.59\times 10^{-3}\left(-x+200\right)$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}=9.59\times 10^{-3}\left(-x+200\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}=9.59\times 10^{-3}\left(-x+200\right)$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$4x^{2}=9.59\times \frac{1}{1000}\left(-x+200\right)$$

Multiply 9.59 and \frac{1}{1000} to get \frac{959}{100000}.

$$4x^{2}=\frac{959}{100000}\left(-x+200\right)$$

Use the distributive property to multiply \frac{959}{100000} by -x+200.

$$4x^{2}=-\frac{959}{100000}x+\frac{959}{500}$$

Add \frac{959}{100000}x to both sides.

$$4x^{2}+\frac{959}{100000}x=\frac{959}{500}$$

Divide both sides by 4.

$$\frac{4x^{2}+\frac{959}{100000}x}{4}=\frac{\frac{959}{500}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{\frac{959}{100000}}{4}x=\frac{\frac{959}{500}}{4}$$

Divide \frac{959}{100000} by 4.

$$x^{2}+\frac{959}{400000}x=\frac{\frac{959}{500}}{4}$$

Divide \frac{959}{500} by 4.

$$x^{2}+\frac{959}{400000}x=\frac{959}{2000}$$

Divide \frac{959}{400000}, the coefficient of the x term, by 2 to get \frac{959}{800000}. Then add the square of \frac{959}{800000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{959}{400000}x+\left(\frac{959}{800000}\right)^{2}=\frac{959}{2000}+\left(\frac{959}{800000}\right)^{2}$$

Square \frac{959}{800000} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{959}{400000}x+\frac{919681}{640000000000}=\frac{959}{2000}+\frac{919681}{640000000000}$$

Add \frac{959}{2000} to \frac{919681}{640000000000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{959}{400000}x+\frac{919681}{640000000000}=\frac{306880919681}{640000000000}$$

Factor x^{2}+\frac{959}{400000}x+\frac{919681}{640000000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{959}{800000}\right)^{2}=\frac{306880919681}{640000000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{959}{800000}\right)^{2}}=\sqrt{\frac{306880919681}{640000000000}}$$

Simplify.

$$x+\frac{959}{800000}=\frac{\sqrt{306880919681}}{800000} x+\frac{959}{800000}=-\frac{\sqrt{306880919681}}{800000}$$

Subtract \frac{959}{800000} from both sides of the equation.

$$x=\frac{\sqrt{306880919681}-959}{800000} x=\frac{-\sqrt{306880919681}-959}{800000}$$