0.5x^2-0.3x+6.858=100

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Solution for 0.5x^2-0.3x+6.858=100 equation: 


Simplifying
0.5x2 + -0.3x + 6.858 = 100

Reorder the terms:
6.858 + -0.3x + 0.5x2 = 100

Solving
6.858 + -0.3x + 0.5x2 = 100

Solving for variable 'x'.

Reorder the terms:
6.858 + -100 + -0.3x + 0.5x2 = 100 + -100

Combine like terms: 6.858 + -100 = -93.142
-93.142 + -0.3x + 0.5x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-93.142 + -0.3x + 0.5x2 = 0

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

Divide each side by '0.5'.
-186.284 + -0.6x + x2 = 0

Move the constant term to the right:

Add '186.284' to each side of the equation.
-186.284 + -0.6x + 186.284 + x2 = 0 + 186.284

Reorder the terms:
-186.284 + 186.284 + -0.6x + x2 = 0 + 186.284

Combine like terms: -186.284 + 186.284 = 0.000
0.000 + -0.6x + x2 = 0 + 186.284
-0.6x + x2 = 0 + 186.284

Combine like terms: 0 + 186.284 = 186.284
-0.6x + x2 = 186.284

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 186.284 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 186.284 + 0.09

Combine like terms: 186.284 + 0.09 = 186.374
0.09 + -0.6x + x2 = 186.374

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 186.374

Calculate the square root of the right side: 13.651886317

Break this problem into two subproblems by setting 
(x + -0.3) equal to 13.651886317 and -13.651886317.


Subproblem 1
x + -0.3 = 13.651886317

Simplifying
x + -0.3 = 13.651886317

Reorder the terms:
-0.3 + x = 13.651886317

Solving
-0.3 + x = 13.651886317

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 13.651886317 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 13.651886317 + 0.3
x = 13.651886317 + 0.3

Combine like terms: 13.651886317 + 0.3 = 13.951886317
x = 13.951886317

Simplifying
x = 13.951886317


Subproblem 2
x + -0.3 = -13.651886317

Simplifying
x + -0.3 = -13.651886317

Reorder the terms:
-0.3 + x = -13.651886317

Solving
-0.3 + x = -13.651886317

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -13.651886317 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -13.651886317 + 0.3
x = -13.651886317 + 0.3

Combine like terms: -13.651886317 + 0.3 = -13.351886317
x = -13.351886317

Simplifying
x = -13.351886317


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.951886317, -13.351886317}

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