Solve 0.7xleft(1-x/750right)-20=0

$$0.7x \left( 1- \frac{ x }{ 750 } \right) -20=0$$

Solve for x

$$x=\frac{25\sqrt{9345}}{7}+375\approx 720.248357811$$

$$x=-\frac{25\sqrt{9345}}{7}+375\approx 29.751642189$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 750.

$$525x\left(1-\frac{x}{750}\right)-15000=0$$

Use the distributive property to multiply 525x by 1-\frac{x}{750}.

$$525x+525x\left(-\frac{x}{750}\right)-15000=0$$

Express 525\left(-\frac{x}{750}\right) as a single fraction.

$$525x+\frac{-525x}{750}x-15000=0$$

Divide -525x by 750 to get -\frac{7}{10}x.

$$525x-\frac{7}{10}xx-15000=0$$

Multiply x and x to get x^{2}.

$$525x-\frac{7}{10}x^{2}-15000=0$$

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.

$$-\frac{7}{10}x^{2}+525x-15000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{7}{10} for a, 525 for b, and -15000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-525±\sqrt{525^{2}-4\left(-\frac{7}{10}\right)\left(-15000\right)}}{2\left(-\frac{7}{10}\right)}$$

Square 525.

$$x=\frac{-525±\sqrt{275625-4\left(-\frac{7}{10}\right)\left(-15000\right)}}{2\left(-\frac{7}{10}\right)}$$

Multiply -4 times -\frac{7}{10}.

$$x=\frac{-525±\sqrt{275625+\frac{14}{5}\left(-15000\right)}}{2\left(-\frac{7}{10}\right)}$$

Multiply \frac{14}{5} times -15000.

$$x=\frac{-525±\sqrt{275625-42000}}{2\left(-\frac{7}{10}\right)}$$

Add 275625 to -42000.

$$x=\frac{-525±\sqrt{233625}}{2\left(-\frac{7}{10}\right)}$$

Take the square root of 233625.

$$x=\frac{-525±5\sqrt{9345}}{2\left(-\frac{7}{10}\right)}$$

Multiply 2 times -\frac{7}{10}.

$$x=\frac{-525±5\sqrt{9345}}{-\frac{7}{5}}$$

Now solve the equation x=\frac{-525±5\sqrt{9345}}{-\frac{7}{5}} when ± is plus. Add -525 to 5\sqrt{9345}.

$$x=\frac{5\sqrt{9345}-525}{-\frac{7}{5}}$$

Divide -525+5\sqrt{9345} by -\frac{7}{5} by multiplying -525+5\sqrt{9345} by the reciprocal of -\frac{7}{5}.

$$x=-\frac{25\sqrt{9345}}{7}+375$$

Now solve the equation x=\frac{-525±5\sqrt{9345}}{-\frac{7}{5}} when ± is minus. Subtract 5\sqrt{9345} from -525.

$$x=\frac{-5\sqrt{9345}-525}{-\frac{7}{5}}$$

Divide -525-5\sqrt{9345} by -\frac{7}{5} by multiplying -525-5\sqrt{9345} by the reciprocal of -\frac{7}{5}.

$$x=\frac{25\sqrt{9345}}{7}+375$$

The equation is now solved.

$$x=-\frac{25\sqrt{9345}}{7}+375 x=\frac{25\sqrt{9345}}{7}+375$$

Steps for Completing the Square

Multiply both sides of the equation by 750.

$$525x\left(1-\frac{x}{750}\right)-15000=0$$

Use the distributive property to multiply 525x by 1-\frac{x}{750}.

$$525x+525x\left(-\frac{x}{750}\right)-15000=0$$

Express 525\left(-\frac{x}{750}\right) as a single fraction.

$$525x+\frac{-525x}{750}x-15000=0$$

Divide -525x by 750 to get -\frac{7}{10}x.

$$525x-\frac{7}{10}xx-15000=0$$

Multiply x and x to get x^{2}.

$$525x-\frac{7}{10}x^{2}-15000=0$$

Add 15000 to both sides. Anything plus zero gives itself.

$$525x-\frac{7}{10}x^{2}=15000$$

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.

$$-\frac{7}{10}x^{2}+525x=15000$$

Divide both sides of the equation by -\frac{7}{10}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{7}{10}x^{2}+525x}{-\frac{7}{10}}=\frac{15000}{-\frac{7}{10}}$$

Dividing by -\frac{7}{10} undoes the multiplication by -\frac{7}{10}.

$$x^{2}+\frac{525}{-\frac{7}{10}}x=\frac{15000}{-\frac{7}{10}}$$

Divide 525 by -\frac{7}{10} by multiplying 525 by the reciprocal of -\frac{7}{10}.

$$x^{2}-750x=\frac{15000}{-\frac{7}{10}}$$

Divide 15000 by -\frac{7}{10} by multiplying 15000 by the reciprocal of -\frac{7}{10}.

$$x^{2}-750x=-\frac{150000}{7}$$

Divide -750, the coefficient of the x term, by 2 to get -375. Then add the square of -375 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-750x+\left(-375\right)^{2}=-\frac{150000}{7}+\left(-375\right)^{2}$$

Square -375.

$$x^{2}-750x+140625=-\frac{150000}{7}+140625$$

Add -\frac{150000}{7} to 140625.

$$x^{2}-750x+140625=\frac{834375}{7}$$

Factor x^{2}-750x+140625. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-375\right)^{2}=\frac{834375}{7}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-375\right)^{2}}=\sqrt{\frac{834375}{7}}$$

Simplify.

$$x-375=\frac{25\sqrt{9345}}{7} x-375=-\frac{25\sqrt{9345}}{7}$$

Add 375 to both sides of the equation.

$$x=\frac{25\sqrt{9345}}{7}+375 x=-\frac{25\sqrt{9345}}{7}+375$$