(6.41)(1.2-x)(x)=(8+2x)(8+2x)

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Solution for (6.41)(1.2-x)(x)=(8+2x)(8+2x) equation: 


Simplifying
(6.41)(1.2 + -1x)(x) = (8 + 2x)(8 + 2x)

Reorder the terms for easier multiplication:
6.41x(1.2 + -1x) = (8 + 2x)(8 + 2x)
(1.2 * 6.41x + -1x * 6.41x) = (8 + 2x)(8 + 2x)
(7.692x + -6.41x2) = (8 + 2x)(8 + 2x)

Multiply (8 + 2x) * (8 + 2x)
7.692x + -6.41x2 = (8(8 + 2x) + 2x * (8 + 2x))
7.692x + -6.41x2 = ((8 * 8 + 2x * 8) + 2x * (8 + 2x))
7.692x + -6.41x2 = ((64 + 16x) + 2x * (8 + 2x))
7.692x + -6.41x2 = (64 + 16x + (8 * 2x + 2x * 2x))
7.692x + -6.41x2 = (64 + 16x + (16x + 4x2))

Combine like terms: 16x + 16x = 32x
7.692x + -6.41x2 = (64 + 32x + 4x2)

Solving
7.692x + -6.41x2 = 64 + 32x + 4x2

Solving for variable 'x'.

Reorder the terms:
-64 + 7.692x + -32x + -6.41x2 + -4x2 = 64 + 32x + 4x2 + -64 + -32x + -4x2

Combine like terms: 7.692x + -32x = -24.308x
-64 + -24.308x + -6.41x2 + -4x2 = 64 + 32x + 4x2 + -64 + -32x + -4x2

Combine like terms: -6.41x2 + -4x2 = -10.41x2
-64 + -24.308x + -10.41x2 = 64 + 32x + 4x2 + -64 + -32x + -4x2

Reorder the terms:
-64 + -24.308x + -10.41x2 = 64 + -64 + 32x + -32x + 4x2 + -4x2

Combine like terms: 64 + -64 = 0
-64 + -24.308x + -10.41x2 = 0 + 32x + -32x + 4x2 + -4x2
-64 + -24.308x + -10.41x2 = 32x + -32x + 4x2 + -4x2

Combine like terms: 32x + -32x = 0
-64 + -24.308x + -10.41x2 = 0 + 4x2 + -4x2
-64 + -24.308x + -10.41x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-64 + -24.308x + -10.41x2 = 0

Begin completing the square.  Divide all terms by
-10.41 the coefficient of the squared term: 

Divide each side by '-10.41'.
6.147934678 + 2.33506244x + x2 = 0

Move the constant term to the right:

Add '-6.147934678' to each side of the equation.
6.147934678 + 2.33506244x + -6.147934678 + x2 = 0 + -6.147934678

Reorder the terms:
6.147934678 + -6.147934678 + 2.33506244x + x2 = 0 + -6.147934678

Combine like terms: 6.147934678 + -6.147934678 = 0.000000000
0.000000000 + 2.33506244x + x2 = 0 + -6.147934678
2.33506244x + x2 = 0 + -6.147934678

Combine like terms: 0 + -6.147934678 = -6.147934678
2.33506244x + x2 = -6.147934678

The x term is 2.33506244x.  Take half its coefficient (1.16753122).
Square it (1.363129150) and add it to both sides.

Add '1.363129150' to each side of the equation.
2.33506244x + 1.363129150 + x2 = -6.147934678 + 1.363129150

Reorder the terms:
1.363129150 + 2.33506244x + x2 = -6.147934678 + 1.363129150

Combine like terms: -6.147934678 + 1.363129150 = -4.784805528
1.363129150 + 2.33506244x + x2 = -4.784805528

Factor a perfect square on the left side:
(x + 1.16753122)(x + 1.16753122) = -4.784805528

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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