2.25x^2-4.20x+1.96=0

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Solution for 2.25x^2-4.20x+1.96=0 equation: 


Simplifying
2.25x2 + -4.20x + 1.96 = 0

Reorder the terms:
1.96 + -4.20x + 2.25x2 = 0

Solving
1.96 + -4.20x + 2.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.25'.
0.8711111111 + -1.866666667x + x2 = 0

Move the constant term to the right:

Add '-0.8711111111' to each side of the equation.
0.8711111111 + -1.866666667x + -0.8711111111 + x2 = 0 + -0.8711111111

Reorder the terms:
0.8711111111 + -0.8711111111 + -1.866666667x + x2 = 0 + -0.8711111111

Combine like terms: 0.8711111111 + -0.8711111111 = 0.0000000000
0.0000000000 + -1.866666667x + x2 = 0 + -0.8711111111
-1.866666667x + x2 = 0 + -0.8711111111

Combine like terms: 0 + -0.8711111111 = -0.8711111111
-1.866666667x + x2 = -0.8711111111

The x term is -1.866666667x.  Take half its coefficient (-0.9333333335).
Square it (0.8711111114) and add it to both sides.

Add '0.8711111114' to each side of the equation.
-1.866666667x + 0.8711111114 + x2 = -0.8711111111 + 0.8711111114

Reorder the terms:
0.8711111114 + -1.866666667x + x2 = -0.8711111111 + 0.8711111114

Combine like terms: -0.8711111111 + 0.8711111114 = 0.0000000003
0.8711111114 + -1.866666667x + x2 = 0.0000000003

Factor a perfect square on the left side:
(x + -0.9333333335)(x + -0.9333333335) = 0.0000000003

Calculate the square root of the right side: 0.000017321

Break this problem into two subproblems by setting 
(x + -0.9333333335) equal to 0.000017321 and -0.000017321.


Subproblem 1
x + -0.9333333335 = 0.000017321

Simplifying
x + -0.9333333335 = 0.000017321

Reorder the terms:
-0.9333333335 + x = 0.000017321

Solving
-0.9333333335 + x = 0.000017321

Solving for variable 'x'.

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

Add '0.9333333335' to each side of the equation.
-0.9333333335 + 0.9333333335 + x = 0.000017321 + 0.9333333335

Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000
0.0000000000 + x = 0.000017321 + 0.9333333335
x = 0.000017321 + 0.9333333335

Combine like terms: 0.000017321 + 0.9333333335 = 0.9333506545
x = 0.9333506545

Simplifying
x = 0.9333506545


Subproblem 2
x + -0.9333333335 = -0.000017321

Simplifying
x + -0.9333333335 = -0.000017321

Reorder the terms:
-0.9333333335 + x = -0.000017321

Solving
-0.9333333335 + x = -0.000017321

Solving for variable 'x'.

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

Add '0.9333333335' to each side of the equation.
-0.9333333335 + 0.9333333335 + x = -0.000017321 + 0.9333333335

Combine like terms: -0.9333333335 + 0.9333333335 = 0.0000000000
0.0000000000 + x = -0.000017321 + 0.9333333335
x = -0.000017321 + 0.9333333335

Combine like terms: -0.000017321 + 0.9333333335 = 0.9333160125
x = 0.9333160125

Simplifying
x = 0.9333160125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9333506545, 0.9333160125}

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