0.2x^2-6.7x-10.5=0

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Solution for 0.2x^2-6.7x-10.5=0 equation: 


Simplifying
0.2x2 + -6.7x + -10.5 = 0

Reorder the terms:
-10.5 + -6.7x + 0.2x2 = 0

Solving
-10.5 + -6.7x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
-52.5 + -33.5x + x2 = 0

Move the constant term to the right:

Add '52.5' to each side of the equation.
-52.5 + -33.5x + 52.5 + x2 = 0 + 52.5

Reorder the terms:
-52.5 + 52.5 + -33.5x + x2 = 0 + 52.5

Combine like terms: -52.5 + 52.5 = 0.0
0.0 + -33.5x + x2 = 0 + 52.5
-33.5x + x2 = 0 + 52.5

Combine like terms: 0 + 52.5 = 52.5
-33.5x + x2 = 52.5

The x term is -33.5x.  Take half its coefficient (-16.75).
Square it (280.5625) and add it to both sides.

Add '280.5625' to each side of the equation.
-33.5x + 280.5625 + x2 = 52.5 + 280.5625

Reorder the terms:
280.5625 + -33.5x + x2 = 52.5 + 280.5625

Combine like terms: 52.5 + 280.5625 = 333.0625
280.5625 + -33.5x + x2 = 333.0625

Factor a perfect square on the left side:
(x + -16.75)(x + -16.75) = 333.0625

Calculate the square root of the right side: 18.25

Break this problem into two subproblems by setting 
(x + -16.75) equal to 18.25 and -18.25.


Subproblem 1
x + -16.75 = 18.25

Simplifying
x + -16.75 = 18.25

Reorder the terms:
-16.75 + x = 18.25

Solving
-16.75 + x = 18.25

Solving for variable 'x'.

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

Add '16.75' to each side of the equation.
-16.75 + 16.75 + x = 18.25 + 16.75

Combine like terms: -16.75 + 16.75 = 0.00
0.00 + x = 18.25 + 16.75
x = 18.25 + 16.75

Combine like terms: 18.25 + 16.75 = 35
x = 35

Simplifying
x = 35


Subproblem 2
x + -16.75 = -18.25

Simplifying
x + -16.75 = -18.25

Reorder the terms:
-16.75 + x = -18.25

Solving
-16.75 + x = -18.25

Solving for variable 'x'.

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

Add '16.75' to each side of the equation.
-16.75 + 16.75 + x = -18.25 + 16.75

Combine like terms: -16.75 + 16.75 = 0.00
0.00 + x = -18.25 + 16.75
x = -18.25 + 16.75

Combine like terms: -18.25 + 16.75 = -1.5
x = -1.5

Simplifying
x = -1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35, -1.5}

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