0=x^2+2.5x-2

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Solution for 0=x^2+2.5x-2 equation: 


Simplifying
0 = x2 + 2.5x + -2

Reorder the terms:
0 = -2 + 2.5x + x2

Solving
0 = -2 + 2.5x + x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -2.5x + -1x2 = -2 + 2.5x + x2 + 2 + -2.5x + -1x2

Reorder the terms:
2 + -2.5x + -1x2 = -2 + 2 + 2.5x + -2.5x + x2 + -1x2

Combine like terms: -2 + 2 = 0
2 + -2.5x + -1x2 = 0 + 2.5x + -2.5x + x2 + -1x2
2 + -2.5x + -1x2 = 2.5x + -2.5x + x2 + -1x2

Combine like terms: 2.5x + -2.5x = 0.0
2 + -2.5x + -1x2 = 0.0 + x2 + -1x2
2 + -2.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -2.5x + -1x2 = 0

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

Divide each side by '-1'.
-2 + 2.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.5x + x2 = 0 + 2
2.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.5x + x2 = 2

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 2 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 2 + 1.5625

Combine like terms: 2 + 1.5625 = 3.5625
1.5625 + 2.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.887458609 and -1.887458609.


Subproblem 1
x + 1.25 = 1.887458609

Simplifying
x + 1.25 = 1.887458609

Reorder the terms:
1.25 + x = 1.887458609

Solving
1.25 + x = 1.887458609

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.887458609 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.887458609 + -1.25
x = 1.887458609 + -1.25

Combine like terms: 1.887458609 + -1.25 = 0.637458609
x = 0.637458609

Simplifying
x = 0.637458609


Subproblem 2
x + 1.25 = -1.887458609

Simplifying
x + 1.25 = -1.887458609

Reorder the terms:
1.25 + x = -1.887458609

Solving
1.25 + x = -1.887458609

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.887458609 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.887458609 + -1.25
x = -1.887458609 + -1.25

Combine like terms: -1.887458609 + -1.25 = -3.137458609
x = -3.137458609

Simplifying
x = -3.137458609


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.637458609, -3.137458609}

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