Solve 174*10^-5=x^2/00100-x

$$174 \times { 10 }^{ -5 } = \frac{ { x }^{ 2 } }{ 00100-x }$$

Solve for x

$$x=-\frac{87}{50000}=-0.00174$$

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.

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

Multiply 174 and \frac{1}{100000} to get \frac{87}{50000}.

$$\frac{87}{50000}x=-x^{2}$$

Add x^{2} to both sides.

$$\frac{87}{50000}x+x^{2}=0$$

Factor out x.

$$x\left(\frac{87}{50000}+x\right)=0$$

To find equation solutions, solve x=0 and \frac{87}{50000}+x=0.

$$x=0 x=-\frac{87}{50000}$$

Variable x cannot be equal to 0.

$$x=-\frac{87}{50000}$$

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.

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

Multiply 174 and \frac{1}{100000} to get \frac{87}{50000}.

$$\frac{87}{50000}x=-x^{2}$$

Add x^{2} to both sides.

$$\frac{87}{50000}x+x^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}+\frac{87}{50000}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, \frac{87}{50000} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{87}{50000}±\sqrt{\left(\frac{87}{50000}\right)^{2}}}{2}$$

Take the square root of \left(\frac{87}{50000}\right)^{2}.

$$x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2}$$

Now solve the equation x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2} when ± is plus. Add -\frac{87}{50000} to \frac{87}{50000} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

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

Divide 0 by 2.

$$x=0$$

Now solve the equation x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2} when ± is minus. Subtract \frac{87}{50000} from -\frac{87}{50000} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{\frac{87}{25000}}{2}$$

Divide -\frac{87}{25000} by 2.

$$x=-\frac{87}{50000}$$

The equation is now solved.

$$x=0 x=-\frac{87}{50000}$$

Variable x cannot be equal to 0.

$$x=-\frac{87}{50000}$$

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.

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

Multiply 174 and \frac{1}{100000} to get \frac{87}{50000}.

$$\frac{87}{50000}x=-x^{2}$$

Add x^{2} to both sides.

$$\frac{87}{50000}x+x^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}+\frac{87}{50000}x=0$$

Divide \frac{87}{50000}, the coefficient of the x term, by 2 to get \frac{87}{100000}. Then add the square of \frac{87}{100000} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{87}{50000}x+\left(\frac{87}{100000}\right)^{2}=\left(\frac{87}{100000}\right)^{2}$$

Square \frac{87}{100000} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{87}{50000}x+\frac{7569}{10000000000}=\frac{7569}{10000000000}$$

Factor x^{2}+\frac{87}{50000}x+\frac{7569}{10000000000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{87}{100000}\right)^{2}=\frac{7569}{10000000000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{87}{100000}\right)^{2}}=\sqrt{\frac{7569}{10000000000}}$$

Simplify.

$$x+\frac{87}{100000}=\frac{87}{100000} x+\frac{87}{100000}=-\frac{87}{100000}$$

Subtract \frac{87}{100000} from both sides of the equation.

$$x=0 x=-\frac{87}{50000}$$

Variable x cannot be equal to 0.

$$x=-\frac{87}{50000}$$