6.8x+2.7=0.8x^2-0.1x

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Solution for 6.8x+2.7=0.8x^2-0.1x equation: 


Simplifying
6.8x + 2.7 = 0.8x2 + -0.1x

Reorder the terms:
2.7 + 6.8x = 0.8x2 + -0.1x

Reorder the terms:
2.7 + 6.8x = -0.1x + 0.8x2

Solving
2.7 + 6.8x = -0.1x + 0.8x2

Solving for variable 'x'.

Combine like terms: 6.8x + 0.1x = 6.9x
2.7 + 6.9x + -0.8x2 = -0.1x + 0.8x2 + 0.1x + -0.8x2

Reorder the terms:
2.7 + 6.9x + -0.8x2 = -0.1x + 0.1x + 0.8x2 + -0.8x2

Combine like terms: -0.1x + 0.1x = 0.0
2.7 + 6.9x + -0.8x2 = 0.0 + 0.8x2 + -0.8x2
2.7 + 6.9x + -0.8x2 = 0.8x2 + -0.8x2

Combine like terms: 0.8x2 + -0.8x2 = 0.0
2.7 + 6.9x + -0.8x2 = 0.0

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
-3.375 + -8.625x + x2 = 0

Move the constant term to the right:

Add '3.375' to each side of the equation.
-3.375 + -8.625x + 3.375 + x2 = 0 + 3.375

Reorder the terms:
-3.375 + 3.375 + -8.625x + x2 = 0 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + -8.625x + x2 = 0 + 3.375
-8.625x + x2 = 0 + 3.375

Combine like terms: 0 + 3.375 = 3.375
-8.625x + x2 = 3.375

The x term is -8.625x.  Take half its coefficient (-4.3125).
Square it (18.59765625) and add it to both sides.

Add '18.59765625' to each side of the equation.
-8.625x + 18.59765625 + x2 = 3.375 + 18.59765625

Reorder the terms:
18.59765625 + -8.625x + x2 = 3.375 + 18.59765625

Combine like terms: 3.375 + 18.59765625 = 21.97265625
18.59765625 + -8.625x + x2 = 21.97265625

Factor a perfect square on the left side:
(x + -4.3125)(x + -4.3125) = 21.97265625

Calculate the square root of the right side: 4.6875

Break this problem into two subproblems by setting 
(x + -4.3125) equal to 4.6875 and -4.6875.


Subproblem 1
x + -4.3125 = 4.6875

Simplifying
x + -4.3125 = 4.6875

Reorder the terms:
-4.3125 + x = 4.6875

Solving
-4.3125 + x = 4.6875

Solving for variable 'x'.

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

Add '4.3125' to each side of the equation.
-4.3125 + 4.3125 + x = 4.6875 + 4.3125

Combine like terms: -4.3125 + 4.3125 = 0.0000
0.0000 + x = 4.6875 + 4.3125
x = 4.6875 + 4.3125

Combine like terms: 4.6875 + 4.3125 = 9
x = 9

Simplifying
x = 9


Subproblem 2
x + -4.3125 = -4.6875

Simplifying
x + -4.3125 = -4.6875

Reorder the terms:
-4.3125 + x = -4.6875

Solving
-4.3125 + x = -4.6875

Solving for variable 'x'.

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

Add '4.3125' to each side of the equation.
-4.3125 + 4.3125 + x = -4.6875 + 4.3125

Combine like terms: -4.3125 + 4.3125 = 0.0000
0.0000 + x = -4.6875 + 4.3125
x = -4.6875 + 4.3125

Combine like terms: -4.6875 + 4.3125 = -0.375
x = -0.375

Simplifying
x = -0.375


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9, -0.375}

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