-6.17=-0.16x^2+0.16x

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Solution for -6.17=-0.16x^2+0.16x equation: 


Simplifying
-6.17 = -0.16x2 + 0.16x

Reorder the terms:
-6.17 = 0.16x + -0.16x2

Solving
-6.17 = 0.16x + -0.16x2

Solving for variable 'x'.

Reorder the terms:
-6.17 + -0.16x + 0.16x2 = 0.16x + -0.16x + -0.16x2 + 0.16x2

Combine like terms: 0.16x + -0.16x = 0.00
-6.17 + -0.16x + 0.16x2 = 0.00 + -0.16x2 + 0.16x2
-6.17 + -0.16x + 0.16x2 = -0.16x2 + 0.16x2

Combine like terms: -0.16x2 + 0.16x2 = 0.00
-6.17 + -0.16x + 0.16x2 = 0.00

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

Divide each side by '0.16'.
-38.5625 + -1x + x2 = 0

Move the constant term to the right:

Add '38.5625' to each side of the equation.
-38.5625 + -1x + 38.5625 + x2 = 0 + 38.5625

Reorder the terms:
-38.5625 + 38.5625 + -1x + x2 = 0 + 38.5625

Combine like terms: -38.5625 + 38.5625 = 0.0000
0.0000 + -1x + x2 = 0 + 38.5625
-1x + x2 = 0 + 38.5625

Combine like terms: 0 + 38.5625 = 38.5625
-1x + x2 = 38.5625

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 38.5625 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 38.5625 + 0.25

Combine like terms: 38.5625 + 0.25 = 38.8125
0.25 + -1x + x2 = 38.8125

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 38.8125

Calculate the square root of the right side: 6.229967897

Break this problem into two subproblems by setting 
(x + -0.5) equal to 6.229967897 and -6.229967897.


Subproblem 1
x + -0.5 = 6.229967897

Simplifying
x + -0.5 = 6.229967897

Reorder the terms:
-0.5 + x = 6.229967897

Solving
-0.5 + x = 6.229967897

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 6.229967897 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 6.229967897 + 0.5
x = 6.229967897 + 0.5

Combine like terms: 6.229967897 + 0.5 = 6.729967897
x = 6.729967897

Simplifying
x = 6.729967897


Subproblem 2
x + -0.5 = -6.229967897

Simplifying
x + -0.5 = -6.229967897

Reorder the terms:
-0.5 + x = -6.229967897

Solving
-0.5 + x = -6.229967897

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -6.229967897 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -6.229967897 + 0.5
x = -6.229967897 + 0.5

Combine like terms: -6.229967897 + 0.5 = -5.729967897
x = -5.729967897

Simplifying
x = -5.729967897


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.729967897, -5.729967897}

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