Solve (40-15*x)*2*x=50

$$(40-15 \times x) \times 2 \times x=50$$

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

$$x=1$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 40-15x by 2.

$$\left(80-30x\right)x=50$$

Use the distributive property to multiply 80-30x by x.

$$80x-30x^{2}=50$$

Subtract 50 from both sides.

$$80x-30x^{2}-50=0$$

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.

$$-30x^{2}+80x-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -30 for a, 80 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-80±\sqrt{80^{2}-4\left(-30\right)\left(-50\right)}}{2\left(-30\right)}$$

Square 80.

$$x=\frac{-80±\sqrt{6400-4\left(-30\right)\left(-50\right)}}{2\left(-30\right)}$$

Multiply -4 times -30.

$$x=\frac{-80±\sqrt{6400+120\left(-50\right)}}{2\left(-30\right)}$$

Multiply 120 times -50.

$$x=\frac{-80±\sqrt{6400-6000}}{2\left(-30\right)}$$

Add 6400 to -6000.

$$x=\frac{-80±\sqrt{400}}{2\left(-30\right)}$$

Take the square root of 400.

$$x=\frac{-80±20}{2\left(-30\right)}$$

Multiply 2 times -30.

$$x=\frac{-80±20}{-60}$$

Now solve the equation x=\frac{-80±20}{-60} when ± is plus. Add -80 to 20.

$$x=-\frac{60}{-60}$$

Divide -60 by -60.

$$x=1$$

Now solve the equation x=\frac{-80±20}{-60} when ± is minus. Subtract 20 from -80.

$$x=-\frac{100}{-60}$$

Reduce the fraction \frac{-100}{-60} to lowest terms by extracting and canceling out 20.

$$x=\frac{5}{3}$$

The equation is now solved.

$$x=1 x=\frac{5}{3}$$

Steps for Completing the Square

Use the distributive property to multiply 40-15x by 2.

$$\left(80-30x\right)x=50$$

Use the distributive property to multiply 80-30x by x.

$$80x-30x^{2}=50$$

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.

$$-30x^{2}+80x=50$$

Divide both sides by -30.

$$\frac{-30x^{2}+80x}{-30}=\frac{50}{-30}$$

Dividing by -30 undoes the multiplication by -30.

$$x^{2}+\frac{80}{-30}x=\frac{50}{-30}$$

Reduce the fraction \frac{80}{-30} to lowest terms by extracting and canceling out 10.

$$x^{2}-\frac{8}{3}x=\frac{50}{-30}$$

Reduce the fraction \frac{50}{-30} to lowest terms by extracting and canceling out 10.

$$x^{2}-\frac{8}{3}x=-\frac{5}{3}$$

Divide -\frac{8}{3}, the coefficient of the x term, by 2 to get -\frac{4}{3}. Then add the square of -\frac{4}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{8}{3}x+\left(-\frac{4}{3}\right)^{2}=-\frac{5}{3}+\left(-\frac{4}{3}\right)^{2}$$

Square -\frac{4}{3} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{8}{3}x+\frac{16}{9}=-\frac{5}{3}+\frac{16}{9}$$

Add -\frac{5}{3} to \frac{16}{9} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{8}{3}x+\frac{16}{9}=\frac{1}{9}$$

Factor x^{2}-\frac{8}{3}x+\frac{16}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{4}{3}\right)^{2}=\frac{1}{9}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{4}{3}\right)^{2}}=\sqrt{\frac{1}{9}}$$

Simplify.

$$x-\frac{4}{3}=\frac{1}{3} x-\frac{4}{3}=-\frac{1}{3}$$

Add \frac{4}{3} to both sides of the equation.

$$x=\frac{5}{3} x=1$$