6.17(-x)(4-x)=(3.8+2x)(3.8+2x)

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Solution for 6.17(-x)(4-x)=(3.8+2x)(3.8+2x) equation: 


Simplifying
6.17(-1x)(4 + -1x) = (3.8 + 2x)(3.8 + 2x)

Remove parenthesis around (-1x)
6.17 * -1x(4 + -1x) = (3.8 + 2x)(3.8 + 2x)

Multiply 6.17 * -1
-6.17x(4 + -1x) = (3.8 + 2x)(3.8 + 2x)
(4 * -6.17x + -1x * -6.17x) = (3.8 + 2x)(3.8 + 2x)
(-24.68x + 6.17x2) = (3.8 + 2x)(3.8 + 2x)

Multiply (3.8 + 2x) * (3.8 + 2x)
-24.68x + 6.17x2 = (3.8(3.8 + 2x) + 2x * (3.8 + 2x))
-24.68x + 6.17x2 = ((3.8 * 3.8 + 2x * 3.8) + 2x * (3.8 + 2x))
-24.68x + 6.17x2 = ((14.44 + 7.6x) + 2x * (3.8 + 2x))
-24.68x + 6.17x2 = (14.44 + 7.6x + (3.8 * 2x + 2x * 2x))
-24.68x + 6.17x2 = (14.44 + 7.6x + (7.6x + 4x2))

Combine like terms: 7.6x + 7.6x = 15.2x
-24.68x + 6.17x2 = (14.44 + 15.2x + 4x2)

Solving
-24.68x + 6.17x2 = 14.44 + 15.2x + 4x2

Solving for variable 'x'.

Reorder the terms:
-14.44 + -24.68x + -15.2x + 6.17x2 + -4x2 = 14.44 + 15.2x + 4x2 + -14.44 + -15.2x + -4x2

Combine like terms: -24.68x + -15.2x = -39.88x
-14.44 + -39.88x + 6.17x2 + -4x2 = 14.44 + 15.2x + 4x2 + -14.44 + -15.2x + -4x2

Combine like terms: 6.17x2 + -4x2 = 2.17x2
-14.44 + -39.88x + 2.17x2 = 14.44 + 15.2x + 4x2 + -14.44 + -15.2x + -4x2

Reorder the terms:
-14.44 + -39.88x + 2.17x2 = 14.44 + -14.44 + 15.2x + -15.2x + 4x2 + -4x2

Combine like terms: 14.44 + -14.44 = 0.00
-14.44 + -39.88x + 2.17x2 = 0.00 + 15.2x + -15.2x + 4x2 + -4x2
-14.44 + -39.88x + 2.17x2 = 15.2x + -15.2x + 4x2 + -4x2

Combine like terms: 15.2x + -15.2x = 0.0
-14.44 + -39.88x + 2.17x2 = 0.0 + 4x2 + -4x2
-14.44 + -39.88x + 2.17x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-14.44 + -39.88x + 2.17x2 = 0

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

Divide each side by '2.17'.
-6.65437788 + -18.37788018x + x2 = 0

Move the constant term to the right:

Add '6.65437788' to each side of the equation.
-6.65437788 + -18.37788018x + 6.65437788 + x2 = 0 + 6.65437788

Reorder the terms:
-6.65437788 + 6.65437788 + -18.37788018x + x2 = 0 + 6.65437788

Combine like terms: -6.65437788 + 6.65437788 = 0.00000000
0.00000000 + -18.37788018x + x2 = 0 + 6.65437788
-18.37788018x + x2 = 0 + 6.65437788

Combine like terms: 0 + 6.65437788 = 6.65437788
-18.37788018x + x2 = 6.65437788

The x term is -18.37788018x.  Take half its coefficient (-9.18894009).
Square it (84.43661998) and add it to both sides.

Add '84.43661998' to each side of the equation.
-18.37788018x + 84.43661998 + x2 = 6.65437788 + 84.43661998

Reorder the terms:
84.43661998 + -18.37788018x + x2 = 6.65437788 + 84.43661998

Combine like terms: 6.65437788 + 84.43661998 = 91.09099786
84.43661998 + -18.37788018x + x2 = 91.09099786

Factor a perfect square on the left side:
(x + -9.18894009)(x + -9.18894009) = 91.09099786

Calculate the square root of the right side: 9.544160406

Break this problem into two subproblems by setting 
(x + -9.18894009) equal to 9.544160406 and -9.544160406.


Subproblem 1
x + -9.18894009 = 9.544160406

Simplifying
x + -9.18894009 = 9.544160406

Reorder the terms:
-9.18894009 + x = 9.544160406

Solving
-9.18894009 + x = 9.544160406

Solving for variable 'x'.

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

Add '9.18894009' to each side of the equation.
-9.18894009 + 9.18894009 + x = 9.544160406 + 9.18894009

Combine like terms: -9.18894009 + 9.18894009 = 0.00000000
0.00000000 + x = 9.544160406 + 9.18894009
x = 9.544160406 + 9.18894009

Combine like terms: 9.544160406 + 9.18894009 = 18.733100496
x = 18.733100496

Simplifying
x = 18.733100496


Subproblem 2
x + -9.18894009 = -9.544160406

Simplifying
x + -9.18894009 = -9.544160406

Reorder the terms:
-9.18894009 + x = -9.544160406

Solving
-9.18894009 + x = -9.544160406

Solving for variable 'x'.

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

Add '9.18894009' to each side of the equation.
-9.18894009 + 9.18894009 + x = -9.544160406 + 9.18894009

Combine like terms: -9.18894009 + 9.18894009 = 0.00000000
0.00000000 + x = -9.544160406 + 9.18894009
x = -9.544160406 + 9.18894009

Combine like terms: -9.544160406 + 9.18894009 = -0.355220316
x = -0.355220316

Simplifying
x = -0.355220316


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.733100496, -0.355220316}

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