Solve 50=0.35*40x(1-0.8540x/5)

$$50 = 0.35 \times 40 x ( 1 - 0.85 \frac { 40 x } { 5 } )$$

Solve for x (complex solution)

$$x=\frac{i\times 5\sqrt{4711}}{476}+\frac{5}{68}\approx 0.073529412+0.720974001i$$

$$x=-\frac{i\times 5\sqrt{4711}}{476}+\frac{5}{68}\approx 0.073529412-0.720974001i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 5.

$$250=1.75\times 40x\left(1-0.85\times \frac{40x}{5}\right)$$

Multiply 1.75 and 40 to get 70.

$$250=70x\left(1-0.85\times \frac{40x}{5}\right)$$

Divide 40x by 5 to get 8x.

$$250=70x\left(1-0.85\times 8x\right)$$

Multiply 0.85 and 8 to get 6.8.

$$250=70x\left(1-6.8x\right)$$

Use the distributive property to multiply 70x by 1-6.8x.

$$250=70x-476x^{2}$$

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

$$70x-476x^{2}=250$$

Subtract 250 from both sides.

$$70x-476x^{2}-250=0$$

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.

$$-476x^{2}+70x-250=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -476 for a, 70 for b, and -250 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-70±\sqrt{70^{2}-4\left(-476\right)\left(-250\right)}}{2\left(-476\right)}$$

Square 70.

$$x=\frac{-70±\sqrt{4900-4\left(-476\right)\left(-250\right)}}{2\left(-476\right)}$$

Multiply -4 times -476.

$$x=\frac{-70±\sqrt{4900+1904\left(-250\right)}}{2\left(-476\right)}$$

Multiply 1904 times -250.

$$x=\frac{-70±\sqrt{4900-476000}}{2\left(-476\right)}$$

Add 4900 to -476000.

$$x=\frac{-70±\sqrt{-471100}}{2\left(-476\right)}$$

Take the square root of -471100.

$$x=\frac{-70±10\sqrt{4711}i}{2\left(-476\right)}$$

Multiply 2 times -476.

$$x=\frac{-70±10\sqrt{4711}i}{-952}$$

Now solve the equation x=\frac{-70±10\sqrt{4711}i}{-952} when ± is plus. Add -70 to 10i\sqrt{4711}.

$$x=\frac{-70+10\sqrt{4711}i}{-952}$$

Divide -70+10i\sqrt{4711} by -952.

$$x=-\frac{5\sqrt{4711}i}{476}+\frac{5}{68}$$

Now solve the equation x=\frac{-70±10\sqrt{4711}i}{-952} when ± is minus. Subtract 10i\sqrt{4711} from -70.

$$x=\frac{-10\sqrt{4711}i-70}{-952}$$

Divide -70-10i\sqrt{4711} by -952.

$$x=\frac{5\sqrt{4711}i}{476}+\frac{5}{68}$$

The equation is now solved.

$$x=-\frac{5\sqrt{4711}i}{476}+\frac{5}{68} x=\frac{5\sqrt{4711}i}{476}+\frac{5}{68}$$

Steps for Completing the Square

Multiply both sides of the equation by 5.

$$250=1.75\times 40x\left(1-0.85\times \frac{40x}{5}\right)$$

Multiply 1.75 and 40 to get 70.

$$250=70x\left(1-0.85\times \frac{40x}{5}\right)$$

Divide 40x by 5 to get 8x.

$$250=70x\left(1-0.85\times 8x\right)$$

Multiply 0.85 and 8 to get 6.8.

$$250=70x\left(1-6.8x\right)$$

Use the distributive property to multiply 70x by 1-6.8x.

$$250=70x-476x^{2}$$

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

$$70x-476x^{2}=250$$

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.

$$-476x^{2}+70x=250$$

Divide both sides by -476.

$$\frac{-476x^{2}+70x}{-476}=\frac{250}{-476}$$

Dividing by -476 undoes the multiplication by -476.

$$x^{2}+\frac{70}{-476}x=\frac{250}{-476}$$

Reduce the fraction \frac{70}{-476} to lowest terms by extracting and canceling out 14.

$$x^{2}-\frac{5}{34}x=\frac{250}{-476}$$

Reduce the fraction \frac{250}{-476} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{5}{34}x=-\frac{125}{238}$$

Divide -\frac{5}{34}, the coefficient of the x term, by 2 to get -\frac{5}{68}. Then add the square of -\frac{5}{68} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{5}{34}x+\left(-\frac{5}{68}\right)^{2}=-\frac{125}{238}+\left(-\frac{5}{68}\right)^{2}$$

Square -\frac{5}{68} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{5}{34}x+\frac{25}{4624}=-\frac{125}{238}+\frac{25}{4624}$$

Add -\frac{125}{238} to \frac{25}{4624} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{5}{34}x+\frac{25}{4624}=-\frac{16825}{32368}$$

Factor x^{2}-\frac{5}{34}x+\frac{25}{4624}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{5}{68}\right)^{2}=-\frac{16825}{32368}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{68}\right)^{2}}=\sqrt{-\frac{16825}{32368}}$$

Simplify.

$$x-\frac{5}{68}=\frac{5\sqrt{4711}i}{476} x-\frac{5}{68}=-\frac{5\sqrt{4711}i}{476}$$

Add \frac{5}{68} to both sides of the equation.

$$x=\frac{5\sqrt{4711}i}{476}+\frac{5}{68} x=-\frac{5\sqrt{4711}i}{476}+\frac{5}{68}$$