Solve x^2/035-x=83176*10^-5

$$\frac{ { x }^{ 2 } }{ 035-x } = 83176 \times { 10 }^{ -5 }$$

Solve for x

$$x=-\frac{10397}{12500}=-0.83176$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-x^{2}=83176\times 10^{-5}x$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$-x^{2}=83176\times \frac{1}{100000}x$$

Multiply 83176 and \frac{1}{100000} to get \frac{10397}{12500}.

$$-x^{2}=\frac{10397}{12500}x$$

Subtract \frac{10397}{12500}x from both sides.

$$-x^{2}-\frac{10397}{12500}x=0$$

Factor out x.

$$x\left(-x-\frac{10397}{12500}\right)=0$$

To find equation solutions, solve x=0 and -x-\frac{10397}{12500}=0.

$$x=0 x=-\frac{10397}{12500}$$

Variable x cannot be equal to 0.

$$x=-\frac{10397}{12500}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-x^{2}=83176\times 10^{-5}x$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$-x^{2}=83176\times \frac{1}{100000}x$$

Multiply 83176 and \frac{1}{100000} to get \frac{10397}{12500}.

$$-x^{2}=\frac{10397}{12500}x$$

Subtract \frac{10397}{12500}x from both sides.

$$-x^{2}-\frac{10397}{12500}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -\frac{10397}{12500} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{10397}{12500}\right)±\sqrt{\left(-\frac{10397}{12500}\right)^{2}}}{2\left(-1\right)}$$

Take the square root of \left(-\frac{10397}{12500}\right)^{2}.

$$x=\frac{-\left(-\frac{10397}{12500}\right)±\frac{10397}{12500}}{2\left(-1\right)}$$

The opposite of -\frac{10397}{12500} is \frac{10397}{12500}.

$$x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{-2}$$

Now solve the equation x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{-2} when ± is plus. Add \frac{10397}{12500} to \frac{10397}{12500} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{10397}{6250}}{-2}$$

Divide \frac{10397}{6250} by -2.

$$x=-\frac{10397}{12500}$$

Now solve the equation x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{-2} when ± is minus. Subtract \frac{10397}{12500} from \frac{10397}{12500} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{-2}$$

Divide 0 by -2.

$$x=0$$

The equation is now solved.

$$x=-\frac{10397}{12500} x=0$$

Variable x cannot be equal to 0.

$$x=-\frac{10397}{12500}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$-x^{2}=83176\times 10^{-5}x$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$-x^{2}=83176\times \frac{1}{100000}x$$

Multiply 83176 and \frac{1}{100000} to get \frac{10397}{12500}.

$$-x^{2}=\frac{10397}{12500}x$$

Subtract \frac{10397}{12500}x from both sides.

$$-x^{2}-\frac{10397}{12500}x=0$$

Divide both sides by -1.

$$\frac{-x^{2}-\frac{10397}{12500}x}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\left(-\frac{\frac{10397}{12500}}{-1}\right)x=\frac{0}{-1}$$

Divide -\frac{10397}{12500} by -1.

$$x^{2}+\frac{10397}{12500}x=\frac{0}{-1}$$

Divide 0 by -1.

$$x^{2}+\frac{10397}{12500}x=0$$

Divide \frac{10397}{12500}, the coefficient of the x term, by 2 to get \frac{10397}{25000}. Then add the square of \frac{10397}{25000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{10397}{12500}x+\left(\frac{10397}{25000}\right)^{2}=\left(\frac{10397}{25000}\right)^{2}$$

Square \frac{10397}{25000} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{108097609}{625000000}$$

Factor x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{10397}{25000}\right)^{2}=\frac{108097609}{625000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{10397}{25000}\right)^{2}}=\sqrt{\frac{108097609}{625000000}}$$

Simplify.

$$x+\frac{10397}{25000}=\frac{10397}{25000} x+\frac{10397}{25000}=-\frac{10397}{25000}$$

Subtract \frac{10397}{25000} from both sides of the equation.

$$x=0 x=-\frac{10397}{12500}$$

Variable x cannot be equal to 0.

$$x=-\frac{10397}{12500}$$