Solve 3x/5left(1-xright)+x+4/2=11left(x-2right)/10

$$\frac{ 3x }{ 5 } \left( 1-x \right) + \frac{ x+4 }{ 2 } = \frac{ 11 \left( x-2 \right) }{ 10 }$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Multiply both sides of the equation by 10, the least common multiple of 5,2,10.

$$2\times 3x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)$$

Multiply 2 and 3 to get 6.

$$6x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)$$

Use the distributive property to multiply 6x by 1-x.

$$6x-6x^{2}+5\left(x+4\right)=11\left(x-2\right)$$

Use the distributive property to multiply 5 by x+4.

$$6x-6x^{2}+5x+20=11\left(x-2\right)$$

Combine 6x and 5x to get 11x.

$$11x-6x^{2}+20=11\left(x-2\right)$$

Use the distributive property to multiply 11 by x-2.

$$11x-6x^{2}+20=11x-22$$

Subtract 11x from both sides.

$$11x-6x^{2}+20-11x=-22$$

Combine 11x and -11x to get 0.

$$-6x^{2}+20=-22$$

Subtract 20 from both sides.

$$-6x^{2}=-22-20$$

Subtract 20 from -22 to get -42.

$$-6x^{2}=-42$$

Divide both sides by -6.

$$x^{2}=\frac{-42}{-6}$$

Divide -42 by -6 to get 7.

$$x^{2}=7$$

Take the square root of both sides of the equation.

$$x=\sqrt{7} x=-\sqrt{7}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 10, the least common multiple of 5,2,10.

$$2\times 3x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)$$

Multiply 2 and 3 to get 6.

$$6x\left(1-x\right)+5\left(x+4\right)=11\left(x-2\right)$$

Use the distributive property to multiply 6x by 1-x.

$$6x-6x^{2}+5\left(x+4\right)=11\left(x-2\right)$$

Use the distributive property to multiply 5 by x+4.

$$6x-6x^{2}+5x+20=11\left(x-2\right)$$

Combine 6x and 5x to get 11x.

$$11x-6x^{2}+20=11\left(x-2\right)$$

Use the distributive property to multiply 11 by x-2.

$$11x-6x^{2}+20=11x-22$$

Subtract 11x from both sides.

$$11x-6x^{2}+20-11x=-22$$

Combine 11x and -11x to get 0.

$$-6x^{2}+20=-22$$

Add 22 to both sides.

$$-6x^{2}+20+22=0$$

Add 20 and 22 to get 42.

$$-6x^{2}+42=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 42}}{2\left(-6\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)\times 42}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24\times 42}}{2\left(-6\right)}$$

Multiply 24 times 42.

$$x=\frac{0±\sqrt{1008}}{2\left(-6\right)}$$

Take the square root of 1008.

$$x=\frac{0±12\sqrt{7}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{0±12\sqrt{7}}{-12}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{-12} when ± is plus.

$$x=-\sqrt{7}$$

Now solve the equation x=\frac{0±12\sqrt{7}}{-12} when ± is minus.

$$x=\sqrt{7}$$

The equation is now solved.

$$x=-\sqrt{7} x=\sqrt{7}$$