5x(x+1)-2x(2x-1)=20

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Solution for 5x(x+1)-2x(2x-1)=20 equation: 


Simplifying
5x(x + 1) + -2x(2x + -1) = 20

Reorder the terms:
5x(1 + x) + -2x(2x + -1) = 20
(1 * 5x + x * 5x) + -2x(2x + -1) = 20
(5x + 5x2) + -2x(2x + -1) = 20

Reorder the terms:
5x + 5x2 + -2x(-1 + 2x) = 20
5x + 5x2 + (-1 * -2x + 2x * -2x) = 20
5x + 5x2 + (2x + -4x2) = 20

Reorder the terms:
5x + 2x + 5x2 + -4x2 = 20

Combine like terms: 5x + 2x = 7x
7x + 5x2 + -4x2 = 20

Combine like terms: 5x2 + -4x2 = 1x2
7x + 1x2 = 20

Solving
7x + 1x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 7x + 1x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 7x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 7x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 7x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 7x + x2 = 0 + 20
7x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
7x + x2 = 20

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 20 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 20 + 12.25

Combine like terms: 20 + 12.25 = 32.25
12.25 + 7x + x2 = 32.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + 3.5 = 5.678908346

Simplifying
x + 3.5 = 5.678908346

Reorder the terms:
3.5 + x = 5.678908346

Solving
3.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.678908346 + -3.5
x = 5.678908346 + -3.5

Combine like terms: 5.678908346 + -3.5 = 2.178908346
x = 2.178908346

Simplifying
x = 2.178908346


Subproblem 2
x + 3.5 = -5.678908346

Simplifying
x + 3.5 = -5.678908346

Reorder the terms:
3.5 + x = -5.678908346

Solving
3.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.678908346 + -3.5
x = -5.678908346 + -3.5

Combine like terms: -5.678908346 + -3.5 = -9.178908346
x = -9.178908346

Simplifying
x = -9.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.178908346, -9.178908346}

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