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

Simple and best practice solution for 2x-3x(x-1)=1 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 2x-3x(x-1)=1 equation: 


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

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

Combine like terms: 2x + 3x = 5x
5x + -3x2 = 1

Solving
5x + -3x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 5x + -3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 5x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.3333333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.666666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.666666667x + x2 = 0 + -0.3333333333
-1.666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.666666667x + x2 = -0.3333333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -0.3333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -0.3333333333 + 0.6944444447

Combine like terms: -0.3333333333 + 0.6944444447 = 0.3611111114
0.6944444447 + -1.666666667x + x2 = 0.3611111114

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.3611111114

Calculate the square root of the right side: 0.600925213

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.600925213 and -0.600925213.


Subproblem 1
x + -0.8333333335 = 0.600925213

Simplifying
x + -0.8333333335 = 0.600925213

Reorder the terms:
-0.8333333335 + x = 0.600925213

Solving
-0.8333333335 + x = 0.600925213

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 0.600925213 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 0.600925213 + 0.8333333335
x = 0.600925213 + 0.8333333335

Combine like terms: 0.600925213 + 0.8333333335 = 1.4342585465
x = 1.4342585465

Simplifying
x = 1.4342585465


Subproblem 2
x + -0.8333333335 = -0.600925213

Simplifying
x + -0.8333333335 = -0.600925213

Reorder the terms:
-0.8333333335 + x = -0.600925213

Solving
-0.8333333335 + x = -0.600925213

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -0.600925213 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -0.600925213 + 0.8333333335
x = -0.600925213 + 0.8333333335

Combine like terms: -0.600925213 + 0.8333333335 = 0.2324081205
x = 0.2324081205

Simplifying
x = 0.2324081205


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4342585465, 0.2324081205}

See similar equations:

| 6x-8y=-11 | | 24/64=x/8 | | -48x+5=-15x | | 5+X*6=29 | | -7X+4=5x-56 | | 11/x=176/160 | | 9+Z*4=17 | | g(x)=-x-2-3 | | g(x)=-sgrtx-2-3 | | 6-14=x | | 3Z+6=27 | | g(x)=-sqrtx-2-3 | | x/18=14/36 | | t^2-3t+2s-23=2s+5 | | 8k+5k=0 | | .6(x+9)=10 | | z^3+4z^2+3z=0 | | l=14-w | | 25/20=5/x | | 10x+12-22x=-10 | | 20/0.25 | | 6/b=3/7 | | 2m-7+4m=-1 | | 10x+26(x-5)=50 | | 12x+7=3x | | 4w^2+108=0 | | 3r-4=81 | | 15/2=4(23)-7 | | 13x-10-7x=-4 | | 26x^2-48x+5=0 | | 3+ax=2x | | 2+9x=65 |

Equations solver categories