200=2*pi*X^2+2*pi*X*6

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Solution for 200=2*pi*X^2+2*pi*X*6 equation:


Simplifying
200 = 2pi * X2 + 2pi * X * 6

Multiply ip * X2
200 = 2ipX2 + 2pi * X * 6

Reorder the terms for easier multiplication:
200 = 2ipX2 + 2 * 6ip * X

Multiply 2 * 6
200 = 2ipX2 + 12ip * X

Multiply ip * X
200 = 2ipX2 + 12ipX

Reorder the terms:
200 = 12ipX + 2ipX2

Solving
200 = 12ipX + 2ipX2

Solving for variable 'i'.

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

Add '-12ipX' to each side of the equation.
200 + -12ipX = 12ipX + -12ipX + 2ipX2

Combine like terms: 12ipX + -12ipX = 0
200 + -12ipX = 0 + 2ipX2
200 + -12ipX = 2ipX2

Add '-2ipX2' to each side of the equation.
200 + -12ipX + -2ipX2 = 2ipX2 + -2ipX2

Combine like terms: 2ipX2 + -2ipX2 = 0
200 + -12ipX + -2ipX2 = 0

Add '-200' to each side of the equation.
200 + -12ipX + -200 + -2ipX2 = 0 + -200

Reorder the terms:
200 + -200 + -12ipX + -2ipX2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -12ipX + -2ipX2 = 0 + -200
-12ipX + -2ipX2 = 0 + -200

Combine like terms: 0 + -200 = -200
-12ipX + -2ipX2 = -200

Reorder the terms:
200 + -12ipX + -2ipX2 = -200 + 200

Combine like terms: -200 + 200 = 0
200 + -12ipX + -2ipX2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -6ipX + -1ipX2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(100 + -6ipX + -1ipX2)' equal to zero and attempt to solve: Simplifying 100 + -6ipX + -1ipX2 = 0 Solving 100 + -6ipX + -1ipX2 = 0 Move all terms containing i to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -6ipX + -100 + -1ipX2 = 0 + -100 Reorder the terms: 100 + -100 + -6ipX + -1ipX2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -6ipX + -1ipX2 = 0 + -100 -6ipX + -1ipX2 = 0 + -100 Combine like terms: 0 + -100 = -100 -6ipX + -1ipX2 = -100 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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