(x+3)-2(x(1+x))=x(2-x)

Simple and best practice solution for (x+3)-2(x(1+x))=x(2-x) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (x+3)-2(x(1+x))=x(2-x) equation:


Simplifying
(x + 3) + -2(x(1 + x)) = x(2 + -1x)

Reorder the terms:
(3 + x) + -2(x(1 + x)) = x(2 + -1x)

Remove parenthesis around (3 + x)
3 + x + -2(x(1 + x)) = x(2 + -1x)
3 + x + -2((1 * x + x * x)) = x(2 + -1x)
3 + x + -2((1x + x2)) = x(2 + -1x)
3 + x + (1x * -2 + x2 * -2) = x(2 + -1x)
3 + x + (-2x + -2x2) = x(2 + -1x)

Combine like terms: x + -2x = -1x
3 + -1x + -2x2 = x(2 + -1x)
3 + -1x + -2x2 = (2 * x + -1x * x)
3 + -1x + -2x2 = (2x + -1x2)

Solving
3 + -1x + -2x2 = 2x + -1x2

Solving for variable 'x'.

Reorder the terms:
3 + -1x + -2x + -2x2 + x2 = 2x + -1x2 + -2x + x2

Combine like terms: -1x + -2x = -3x
3 + -3x + -2x2 + x2 = 2x + -1x2 + -2x + x2

Combine like terms: -2x2 + x2 = -1x2
3 + -3x + -1x2 = 2x + -1x2 + -2x + x2

Reorder the terms:
3 + -3x + -1x2 = 2x + -2x + -1x2 + x2

Combine like terms: 2x + -2x = 0
3 + -3x + -1x2 = 0 + -1x2 + x2
3 + -3x + -1x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
3 + -3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + 3x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 3x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3x + x2 = 0 + 3
3x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
3x + x2 = 3

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 3 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + 3x + x2 = 5.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + 1.5 = 2.291287847 Simplifying x + 1.5 = 2.291287847 Reorder the terms: 1.5 + x = 2.291287847 Solving 1.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.291287847 + -1.5 x = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 x = 0.791287847 Simplifying x = 0.791287847

Subproblem 2

x + 1.5 = -2.291287847 Simplifying x + 1.5 = -2.291287847 Reorder the terms: 1.5 + x = -2.291287847 Solving 1.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.291287847 + -1.5 x = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 x = -3.791287847 Simplifying x = -3.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.791287847, -3.791287847}

See similar equations:

| 8x+7y=416 | | (2/3)y=16/27 | | -11/5(-6) | | x+x+14=90 | | 10b^2+6b=0 | | x+x+x=14 | | [(-23)+(-7)]+13= | | 7+6(-3)= | | 9y-4-5y=5y-1 | | 6.5(y-4)=5.2-y | | 144=x^2-18x | | Y=-9x^2+54x+8 | | 7+6(-6)= | | 4u-8u=-8-20 | | n+(n+24)+1/2(n+24)=76 | | y=20-3(-8) | | x^2+y^2-10x-14y-5=0 | | Y=-9x+54x-8 | | -1/4(-9y+36) | | 5x-9=x-1 | | 7y-6=5+11y | | 48x^2+48y^2-32x+24y-13=0 | | 2x-2=100 | | 2x-2=20.8567849 | | 8x=-14 | | 2x=-4y | | x^2-6x+9=6 | | 7(2x-3)+5x=19-x | | x^2-10x-250=0 | | 8x^2+16x-5=0 | | -25+13z+13k-5z-4k+19= | | 5/3x+1/3x=2x+7/3+7/3x |

Equations solver categories