x^2-4.27x+3.07=0

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Solution for x^2-4.27x+3.07=0 equation: 


Simplifying
x2 + -4.27x + 3.07 = 0

Reorder the terms:
3.07 + -4.27x + x2 = 0

Solving
3.07 + -4.27x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3.07' to each side of the equation.
3.07 + -4.27x + -3.07 + x2 = 0 + -3.07

Reorder the terms:
3.07 + -3.07 + -4.27x + x2 = 0 + -3.07

Combine like terms: 3.07 + -3.07 = 0.00
0.00 + -4.27x + x2 = 0 + -3.07
-4.27x + x2 = 0 + -3.07

Combine like terms: 0 + -3.07 = -3.07
-4.27x + x2 = -3.07

The x term is -4.27x.  Take half its coefficient (-2.135).
Square it (4.558225) and add it to both sides.

Add '4.558225' to each side of the equation.
-4.27x + 4.558225 + x2 = -3.07 + 4.558225

Reorder the terms:
4.558225 + -4.27x + x2 = -3.07 + 4.558225

Combine like terms: -3.07 + 4.558225 = 1.488225
4.558225 + -4.27x + x2 = 1.488225

Factor a perfect square on the left side:
(x + -2.135)(x + -2.135) = 1.488225

Calculate the square root of the right side: 1.219928277

Break this problem into two subproblems by setting 
(x + -2.135) equal to 1.219928277 and -1.219928277.


Subproblem 1
x + -2.135 = 1.219928277

Simplifying
x + -2.135 = 1.219928277

Reorder the terms:
-2.135 + x = 1.219928277

Solving
-2.135 + x = 1.219928277

Solving for variable 'x'.

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

Add '2.135' to each side of the equation.
-2.135 + 2.135 + x = 1.219928277 + 2.135

Combine like terms: -2.135 + 2.135 = 0.000
0.000 + x = 1.219928277 + 2.135
x = 1.219928277 + 2.135

Combine like terms: 1.219928277 + 2.135 = 3.354928277
x = 3.354928277

Simplifying
x = 3.354928277


Subproblem 2
x + -2.135 = -1.219928277

Simplifying
x + -2.135 = -1.219928277

Reorder the terms:
-2.135 + x = -1.219928277

Solving
-2.135 + x = -1.219928277

Solving for variable 'x'.

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

Add '2.135' to each side of the equation.
-2.135 + 2.135 + x = -1.219928277 + 2.135

Combine like terms: -2.135 + 2.135 = 0.000
0.000 + x = -1.219928277 + 2.135
x = -1.219928277 + 2.135

Combine like terms: -1.219928277 + 2.135 = 0.915071723
x = 0.915071723

Simplifying
x = 0.915071723


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.354928277, 0.915071723}

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