Solve 30000=(x-60)*(-100x+10000)

$$30000 = ( x - 60 ) \cdot ( - 100 x + 10000 )$$

Solve for x

$$x=70$$

$$x=90$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-60 by -100x+10000 and combine like terms.

$$30000=-100x^{2}+16000x-600000$$

Swap sides so that all variable terms are on the left hand side.

$$-100x^{2}+16000x-600000=30000$$

Subtract 30000 from both sides.

$$-100x^{2}+16000x-600000-30000=0$$

Subtract 30000 from -600000 to get -630000.

$$-100x^{2}+16000x-630000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -100 for a, 16000 for b, and -630000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16000±\sqrt{16000^{2}-4\left(-100\right)\left(-630000\right)}}{2\left(-100\right)}$$

Square 16000.

$$x=\frac{-16000±\sqrt{256000000-4\left(-100\right)\left(-630000\right)}}{2\left(-100\right)}$$

Multiply -4 times -100.

$$x=\frac{-16000±\sqrt{256000000+400\left(-630000\right)}}{2\left(-100\right)}$$

Multiply 400 times -630000.

$$x=\frac{-16000±\sqrt{256000000-252000000}}{2\left(-100\right)}$$

Add 256000000 to -252000000.

$$x=\frac{-16000±\sqrt{4000000}}{2\left(-100\right)}$$

Take the square root of 4000000.

$$x=\frac{-16000±2000}{2\left(-100\right)}$$

Multiply 2 times -100.

$$x=\frac{-16000±2000}{-200}$$

Now solve the equation x=\frac{-16000±2000}{-200} when ± is plus. Add -16000 to 2000.

$$x=-\frac{14000}{-200}$$

Divide -14000 by -200.

$$x=70$$

Now solve the equation x=\frac{-16000±2000}{-200} when ± is minus. Subtract 2000 from -16000.

$$x=-\frac{18000}{-200}$$

Divide -18000 by -200.

$$x=90$$

The equation is now solved.

$$x=70 x=90$$

Steps for Completing the Square

Use the distributive property to multiply x-60 by -100x+10000 and combine like terms.

$$30000=-100x^{2}+16000x-600000$$

Swap sides so that all variable terms are on the left hand side.

$$-100x^{2}+16000x-600000=30000$$

Add 600000 to both sides.

$$-100x^{2}+16000x=30000+600000$$

Add 30000 and 600000 to get 630000.

$$-100x^{2}+16000x=630000$$

Divide both sides by -100.

$$\frac{-100x^{2}+16000x}{-100}=\frac{630000}{-100}$$

Dividing by -100 undoes the multiplication by -100.

$$x^{2}+\frac{16000}{-100}x=\frac{630000}{-100}$$

Divide 16000 by -100.

$$x^{2}-160x=\frac{630000}{-100}$$

Divide 630000 by -100.

$$x^{2}-160x=-6300$$

Divide -160, the coefficient of the x term, by 2 to get -80. Then add the square of -80 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-160x+\left(-80\right)^{2}=-6300+\left(-80\right)^{2}$$

Square -80.

$$x^{2}-160x+6400=-6300+6400$$

Add -6300 to 6400.

$$x^{2}-160x+6400=100$$

Factor x^{2}-160x+6400. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-80\right)^{2}=100$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-80\right)^{2}}=\sqrt{100}$$

Simplify.

$$x-80=10 x-80=-10$$

Add 80 to both sides of the equation.

$$x=90 x=70$$