0.225x^2+1.5x-2.5=0

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Solution for 0.225x^2+1.5x-2.5=0 equation: 


Simplifying
0.225x2 + 1.5x + -2.5 = 0

Reorder the terms:
-2.5 + 1.5x + 0.225x2 = 0

Solving
-2.5 + 1.5x + 0.225x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.225'.
-11.11111111 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '11.11111111' to each side of the equation.
-11.11111111 + 6.666666667x + 11.11111111 + x2 = 0 + 11.11111111

Reorder the terms:
-11.11111111 + 11.11111111 + 6.666666667x + x2 = 0 + 11.11111111

Combine like terms: -11.11111111 + 11.11111111 = 0.00000000
0.00000000 + 6.666666667x + x2 = 0 + 11.11111111
6.666666667x + x2 = 0 + 11.11111111

Combine like terms: 0 + 11.11111111 = 11.11111111
6.666666667x + x2 = 11.11111111

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 11.11111111 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 11.11111111 + 11.11111112

Combine like terms: 11.11111111 + 11.11111112 = 22.22222223
11.11111112 + 6.666666667x + x2 = 22.22222223

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 22.22222223

Calculate the square root of the right side: 4.714045209

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 4.714045209 and -4.714045209.


Subproblem 1
x + 3.333333334 = 4.714045209

Simplifying
x + 3.333333334 = 4.714045209

Reorder the terms:
3.333333334 + x = 4.714045209

Solving
3.333333334 + x = 4.714045209

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 4.714045209 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 4.714045209 + -3.333333334
x = 4.714045209 + -3.333333334

Combine like terms: 4.714045209 + -3.333333334 = 1.380711875
x = 1.380711875

Simplifying
x = 1.380711875


Subproblem 2
x + 3.333333334 = -4.714045209

Simplifying
x + 3.333333334 = -4.714045209

Reorder the terms:
3.333333334 + x = -4.714045209

Solving
3.333333334 + x = -4.714045209

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -4.714045209 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -4.714045209 + -3.333333334
x = -4.714045209 + -3.333333334

Combine like terms: -4.714045209 + -3.333333334 = -8.047378543
x = -8.047378543

Simplifying
x = -8.047378543


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.380711875, -8.047378543}

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