-1.86x^2+10x-8.14=0

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Solution for -1.86x^2+10x-8.14=0 equation: 


Simplifying
-1.86x2 + 10x + -8.14 = 0

Reorder the terms:
-8.14 + 10x + -1.86x2 = 0

Solving
-8.14 + 10x + -1.86x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.86 the coefficient of the squared term: 

Divide each side by '-1.86'.
4.376344086 + -5.376344086x + x2 = 0

Move the constant term to the right:

Add '-4.376344086' to each side of the equation.
4.376344086 + -5.376344086x + -4.376344086 + x2 = 0 + -4.376344086

Reorder the terms:
4.376344086 + -4.376344086 + -5.376344086x + x2 = 0 + -4.376344086

Combine like terms: 4.376344086 + -4.376344086 = 0.000000000
0.000000000 + -5.376344086x + x2 = 0 + -4.376344086
-5.376344086x + x2 = 0 + -4.376344086

Combine like terms: 0 + -4.376344086 = -4.376344086
-5.376344086x + x2 = -4.376344086

The x term is -5.376344086x.  Take half its coefficient (-2.688172043).
Square it (7.226268933) and add it to both sides.

Add '7.226268933' to each side of the equation.
-5.376344086x + 7.226268933 + x2 = -4.376344086 + 7.226268933

Reorder the terms:
7.226268933 + -5.376344086x + x2 = -4.376344086 + 7.226268933

Combine like terms: -4.376344086 + 7.226268933 = 2.849924847
7.226268933 + -5.376344086x + x2 = 2.849924847

Factor a perfect square on the left side:
(x + -2.688172043)(x + -2.688172043) = 2.849924847

Calculate the square root of the right side: 1.688172043

Break this problem into two subproblems by setting 
(x + -2.688172043) equal to 1.688172043 and -1.688172043.


Subproblem 1
x + -2.688172043 = 1.688172043

Simplifying
x + -2.688172043 = 1.688172043

Reorder the terms:
-2.688172043 + x = 1.688172043

Solving
-2.688172043 + x = 1.688172043

Solving for variable 'x'.

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

Add '2.688172043' to each side of the equation.
-2.688172043 + 2.688172043 + x = 1.688172043 + 2.688172043

Combine like terms: -2.688172043 + 2.688172043 = 0.000000000
0.000000000 + x = 1.688172043 + 2.688172043
x = 1.688172043 + 2.688172043

Combine like terms: 1.688172043 + 2.688172043 = 4.376344086
x = 4.376344086

Simplifying
x = 4.376344086


Subproblem 2
x + -2.688172043 = -1.688172043

Simplifying
x + -2.688172043 = -1.688172043

Reorder the terms:
-2.688172043 + x = -1.688172043

Solving
-2.688172043 + x = -1.688172043

Solving for variable 'x'.

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

Add '2.688172043' to each side of the equation.
-2.688172043 + 2.688172043 + x = -1.688172043 + 2.688172043

Combine like terms: -2.688172043 + 2.688172043 = 0.000000000
0.000000000 + x = -1.688172043 + 2.688172043
x = -1.688172043 + 2.688172043

Combine like terms: -1.688172043 + 2.688172043 = 1
x = 1

Simplifying
x = 1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.376344086, 1}

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