1.2x^2+2.5x=1.8

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Solution for 1.2x^2+2.5x=1.8 equation: 


Simplifying
1.2x2 + 2.5x = 1.8

Reorder the terms:
2.5x + 1.2x2 = 1.8

Solving
2.5x + 1.2x2 = 1.8

Solving for variable 'x'.

Reorder the terms:
-1.8 + 2.5x + 1.2x2 = 1.8 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
-1.8 + 2.5x + 1.2x2 = 0.0

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

Divide each side by '1.2'.
-1.5 + 2.083333333x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2.083333333x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2.083333333x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2.083333333x + x2 = 0 + 1.5
2.083333333x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2.083333333x + x2 = 1.5

The x term is 2.083333333x.  Take half its coefficient (1.041666667).
Square it (1.085069445) and add it to both sides.

Add '1.085069445' to each side of the equation.
2.083333333x + 1.085069445 + x2 = 1.5 + 1.085069445

Reorder the terms:
1.085069445 + 2.083333333x + x2 = 1.5 + 1.085069445

Combine like terms: 1.5 + 1.085069445 = 2.585069445
1.085069445 + 2.083333333x + x2 = 2.585069445

Factor a perfect square on the left side:
(x + 1.041666667)(x + 1.041666667) = 2.585069445

Calculate the square root of the right side: 1.607815115

Break this problem into two subproblems by setting 
(x + 1.041666667) equal to 1.607815115 and -1.607815115.


Subproblem 1
x + 1.041666667 = 1.607815115

Simplifying
x + 1.041666667 = 1.607815115

Reorder the terms:
1.041666667 + x = 1.607815115

Solving
1.041666667 + x = 1.607815115

Solving for variable 'x'.

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

Add '-1.041666667' to each side of the equation.
1.041666667 + -1.041666667 + x = 1.607815115 + -1.041666667

Combine like terms: 1.041666667 + -1.041666667 = 0.000000000
0.000000000 + x = 1.607815115 + -1.041666667
x = 1.607815115 + -1.041666667

Combine like terms: 1.607815115 + -1.041666667 = 0.566148448
x = 0.566148448

Simplifying
x = 0.566148448


Subproblem 2
x + 1.041666667 = -1.607815115

Simplifying
x + 1.041666667 = -1.607815115

Reorder the terms:
1.041666667 + x = -1.607815115

Solving
1.041666667 + x = -1.607815115

Solving for variable 'x'.

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

Add '-1.041666667' to each side of the equation.
1.041666667 + -1.041666667 + x = -1.607815115 + -1.041666667

Combine like terms: 1.041666667 + -1.041666667 = 0.000000000
0.000000000 + x = -1.607815115 + -1.041666667
x = -1.607815115 + -1.041666667

Combine like terms: -1.607815115 + -1.041666667 = -2.649481782
x = -2.649481782

Simplifying
x = -2.649481782


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.566148448, -2.649481782}

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