0.69696969x^2-3x+2.25=0

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Solution for 0.69696969x^2-3x+2.25=0 equation: 


Simplifying
0.69696969x2 + -3x + 2.25 = 0

Reorder the terms:
2.25 + -3x + 0.69696969x2 = 0

Solving
2.25 + -3x + 0.69696969x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.69696969 the coefficient of the squared term: 

Divide each side by '0.69696969'.
3.228260902 + -4.304347869x + x2 = 0

Move the constant term to the right:

Add '-3.228260902' to each side of the equation.
3.228260902 + -4.304347869x + -3.228260902 + x2 = 0 + -3.228260902

Reorder the terms:
3.228260902 + -3.228260902 + -4.304347869x + x2 = 0 + -3.228260902

Combine like terms: 3.228260902 + -3.228260902 = 0.000000000
0.000000000 + -4.304347869x + x2 = 0 + -3.228260902
-4.304347869x + x2 = 0 + -3.228260902

Combine like terms: 0 + -3.228260902 = -3.228260902
-4.304347869x + x2 = -3.228260902

The x term is -4.304347869x.  Take half its coefficient (-2.152173935).
Square it (4.631852646) and add it to both sides.

Add '4.631852646' to each side of the equation.
-4.304347869x + 4.631852646 + x2 = -3.228260902 + 4.631852646

Reorder the terms:
4.631852646 + -4.304347869x + x2 = -3.228260902 + 4.631852646

Combine like terms: -3.228260902 + 4.631852646 = 1.403591744
4.631852646 + -4.304347869x + x2 = 1.403591744

Factor a perfect square on the left side:
(x + -2.152173935)(x + -2.152173935) = 1.403591744

Calculate the square root of the right side: 1.184732773

Break this problem into two subproblems by setting 
(x + -2.152173935) equal to 1.184732773 and -1.184732773.


Subproblem 1
x + -2.152173935 = 1.184732773

Simplifying
x + -2.152173935 = 1.184732773

Reorder the terms:
-2.152173935 + x = 1.184732773

Solving
-2.152173935 + x = 1.184732773

Solving for variable 'x'.

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

Add '2.152173935' to each side of the equation.
-2.152173935 + 2.152173935 + x = 1.184732773 + 2.152173935

Combine like terms: -2.152173935 + 2.152173935 = 0.000000000
0.000000000 + x = 1.184732773 + 2.152173935
x = 1.184732773 + 2.152173935

Combine like terms: 1.184732773 + 2.152173935 = 3.336906708
x = 3.336906708

Simplifying
x = 3.336906708


Subproblem 2
x + -2.152173935 = -1.184732773

Simplifying
x + -2.152173935 = -1.184732773

Reorder the terms:
-2.152173935 + x = -1.184732773

Solving
-2.152173935 + x = -1.184732773

Solving for variable 'x'.

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

Add '2.152173935' to each side of the equation.
-2.152173935 + 2.152173935 + x = -1.184732773 + 2.152173935

Combine like terms: -2.152173935 + 2.152173935 = 0.000000000
0.000000000 + x = -1.184732773 + 2.152173935
x = -1.184732773 + 2.152173935

Combine like terms: -1.184732773 + 2.152173935 = 0.967441162
x = 0.967441162

Simplifying
x = 0.967441162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.336906708, 0.967441162}

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