x=1.5-x-2.5x-x^2

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Solution for x=1.5-x-2.5x-x^2 equation: 


Simplifying
x = 1.5 + -1x + -2.5x + -1x2

Combine like terms: -1x + -2.5x = -3.5x
x = 1.5 + -3.5x + -1x2

Solving
x = 1.5 + -3.5x + -1x2

Solving for variable 'x'.

Reorder the terms:
-1.5 + x + 3.5x + x2 = 1.5 + -3.5x + -1x2 + -1.5 + 3.5x + x2

Combine like terms: x + 3.5x = 4.5x
-1.5 + 4.5x + x2 = 1.5 + -3.5x + -1x2 + -1.5 + 3.5x + x2

Reorder the terms:
-1.5 + 4.5x + x2 = 1.5 + -1.5 + -3.5x + 3.5x + -1x2 + x2

Combine like terms: 1.5 + -1.5 = 0.0
-1.5 + 4.5x + x2 = 0.0 + -3.5x + 3.5x + -1x2 + x2
-1.5 + 4.5x + x2 = -3.5x + 3.5x + -1x2 + x2

Combine like terms: -3.5x + 3.5x = 0.0
-1.5 + 4.5x + x2 = 0.0 + -1x2 + x2
-1.5 + 4.5x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-1.5 + 4.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4.5x + x2 = 0 + 1.5
4.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4.5x + x2 = 1.5

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 1.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 1.5 + 5.0625

Combine like terms: 1.5 + 5.0625 = 6.5625
5.0625 + 4.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.561737691 and -2.561737691.


Subproblem 1
x + 2.25 = 2.561737691

Simplifying
x + 2.25 = 2.561737691

Reorder the terms:
2.25 + x = 2.561737691

Solving
2.25 + x = 2.561737691

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.561737691 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.561737691 + -2.25
x = 2.561737691 + -2.25

Combine like terms: 2.561737691 + -2.25 = 0.311737691
x = 0.311737691

Simplifying
x = 0.311737691


Subproblem 2
x + 2.25 = -2.561737691

Simplifying
x + 2.25 = -2.561737691

Reorder the terms:
2.25 + x = -2.561737691

Solving
2.25 + x = -2.561737691

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.561737691 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.561737691 + -2.25
x = -2.561737691 + -2.25

Combine like terms: -2.561737691 + -2.25 = -4.811737691
x = -4.811737691

Simplifying
x = -4.811737691


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.311737691, -4.811737691}

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