2x(x-1)+3(x+1)=10

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Solution for 2x(x-1)+3(x+1)=10 equation: 


Simplifying
2x(x + -1) + 3(x + 1) = 10

Reorder the terms:
2x(-1 + x) + 3(x + 1) = 10
(-1 * 2x + x * 2x) + 3(x + 1) = 10
(-2x + 2x2) + 3(x + 1) = 10

Reorder the terms:
-2x + 2x2 + 3(1 + x) = 10
-2x + 2x2 + (1 * 3 + x * 3) = 10
-2x + 2x2 + (3 + 3x) = 10

Reorder the terms:
3 + -2x + 3x + 2x2 = 10

Combine like terms: -2x + 3x = 1x
3 + 1x + 2x2 = 10

Solving
3 + 1x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
3 + -10 + 1x + 2x2 = 10 + -10

Combine like terms: 3 + -10 = -7
-7 + 1x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-7 + 1x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 0.5x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 0.5x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 0.5x + x2 = 0 + 3.5
0.5x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
0.5x + x2 = 3.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 3.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 3.5 + 0.0625

Combine like terms: 3.5 + 0.0625 = 3.5625
0.0625 + 0.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.887458609 and -1.887458609.


Subproblem 1
x + 0.25 = 1.887458609

Simplifying
x + 0.25 = 1.887458609

Reorder the terms:
0.25 + x = 1.887458609

Solving
0.25 + x = 1.887458609

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.887458609 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.887458609 + -0.25
x = 1.887458609 + -0.25

Combine like terms: 1.887458609 + -0.25 = 1.637458609
x = 1.637458609

Simplifying
x = 1.637458609


Subproblem 2
x + 0.25 = -1.887458609

Simplifying
x + 0.25 = -1.887458609

Reorder the terms:
0.25 + x = -1.887458609

Solving
0.25 + x = -1.887458609

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.887458609 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.887458609 + -0.25
x = -1.887458609 + -0.25

Combine like terms: -1.887458609 + -0.25 = -2.137458609
x = -2.137458609

Simplifying
x = -2.137458609


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.637458609, -2.137458609}

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