Solve x^2/(10-x)=1*10^5

$$\frac { x ^ { 2 } } { ( 10 - x ) } = 1 \times 10 ^ { 5 }$$

Solve for x

$$x=1000\sqrt{2501}-50000\approx 9.9990002$$

$$x=-1000\sqrt{2501}-50000\approx -100009.9990002$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 10 since division by zero is not defined. Multiply both sides of the equation by -x+10.

$$x^{2}=1\times 10^{5}\left(-x+10\right)$$

Calculate 10 to the power of 5 and get 100000.

$$x^{2}=1\times 100000\left(-x+10\right)$$

Multiply 1 and 100000 to get 100000.

$$x^{2}=100000\left(-x+10\right)$$

Use the distributive property to multiply 100000 by -x+10.

$$x^{2}=-100000x+1000000$$

Add 100000x to both sides.

$$x^{2}+100000x=1000000$$

Subtract 1000000 from both sides.

$$x^{2}+100000x-1000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 100000 for b, and -1000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-100000±\sqrt{100000^{2}-4\left(-1000000\right)}}{2}$$

Square 100000.

$$x=\frac{-100000±\sqrt{10000000000-4\left(-1000000\right)}}{2}$$

Multiply -4 times -1000000.

$$x=\frac{-100000±\sqrt{10000000000+4000000}}{2}$$

Add 10000000000 to 4000000.

$$x=\frac{-100000±\sqrt{10004000000}}{2}$$

Take the square root of 10004000000.

$$x=\frac{-100000±2000\sqrt{2501}}{2}$$

Now solve the equation x=\frac{-100000±2000\sqrt{2501}}{2} when ± is plus. Add -100000 to 2000\sqrt{2501}.

$$x=\frac{2000\sqrt{2501}-100000}{2}$$

Divide -100000+2000\sqrt{2501} by 2.

$$x=1000\sqrt{2501}-50000$$

Now solve the equation x=\frac{-100000±2000\sqrt{2501}}{2} when ± is minus. Subtract 2000\sqrt{2501} from -100000.

$$x=\frac{-2000\sqrt{2501}-100000}{2}$$

Divide -100000-2000\sqrt{2501} by 2.

$$x=-1000\sqrt{2501}-50000$$

The equation is now solved.

$$x=1000\sqrt{2501}-50000 x=-1000\sqrt{2501}-50000$$

Steps for Completing the Square

Variable x cannot be equal to 10 since division by zero is not defined. Multiply both sides of the equation by -x+10.

$$x^{2}=1\times 10^{5}\left(-x+10\right)$$

Calculate 10 to the power of 5 and get 100000.

$$x^{2}=1\times 100000\left(-x+10\right)$$

Multiply 1 and 100000 to get 100000.

$$x^{2}=100000\left(-x+10\right)$$

Use the distributive property to multiply 100000 by -x+10.

$$x^{2}=-100000x+1000000$$

Add 100000x to both sides.

$$x^{2}+100000x=1000000$$

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

$$x^{2}+100000x+50000^{2}=1000000+50000^{2}$$

Square 50000.

$$x^{2}+100000x+2500000000=1000000+2500000000$$

Add 1000000 to 2500000000.

$$x^{2}+100000x+2500000000=2501000000$$

Factor x^{2}+100000x+2500000000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+50000\right)^{2}=2501000000$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+50000\right)^{2}}=\sqrt{2501000000}$$

Simplify.

$$x+50000=1000\sqrt{2501} x+50000=-1000\sqrt{2501}$$

Subtract 50000 from both sides of the equation.

$$x=1000\sqrt{2501}-50000 x=-1000\sqrt{2501}-50000$$