28.1=114I-100I^2

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Solution for 28.1=114I-100I^2 equation:


Simplifying
28.1 = 114I + -100I2

Solving
28.1 = 114I + -100I2

Solving for variable 'I'.

Reorder the terms:
28.1 + -114I + 100I2 = 114I + -114I + -100I2 + 100I2

Combine like terms: 114I + -114I = 0
28.1 + -114I + 100I2 = 0 + -100I2 + 100I2
28.1 + -114I + 100I2 = -100I2 + 100I2

Combine like terms: -100I2 + 100I2 = 0
28.1 + -114I + 100I2 = 0

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

Divide each side by '100'.
0.281 + -1.14I + I2 = 0

Move the constant term to the right:

Add '-0.281' to each side of the equation.
0.281 + -1.14I + -0.281 + I2 = 0 + -0.281

Reorder the terms:
0.281 + -0.281 + -1.14I + I2 = 0 + -0.281

Combine like terms: 0.281 + -0.281 = 0.000
0.000 + -1.14I + I2 = 0 + -0.281
-1.14I + I2 = 0 + -0.281

Combine like terms: 0 + -0.281 = -0.281
-1.14I + I2 = -0.281

The I term is -1.14I.  Take half its coefficient (-0.57).
Square it (0.3249) and add it to both sides.

Add '0.3249' to each side of the equation.
-1.14I + 0.3249 + I2 = -0.281 + 0.3249

Reorder the terms:
0.3249 + -1.14I + I2 = -0.281 + 0.3249

Combine like terms: -0.281 + 0.3249 = 0.0439
0.3249 + -1.14I + I2 = 0.0439

Factor a perfect square on the left side:
(I + -0.57)(I + -0.57) = 0.0439

Calculate the square root of the right side: 0.209523268

Break this problem into two subproblems by setting 
(I + -0.57) equal to 0.209523268 and -0.209523268.

Subproblem 1

I + -0.57 = 0.209523268 Simplifying I + -0.57 = 0.209523268 Reorder the terms: -0.57 + I = 0.209523268 Solving -0.57 + I = 0.209523268 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '0.57' to each side of the equation. -0.57 + 0.57 + I = 0.209523268 + 0.57 Combine like terms: -0.57 + 0.57 = 0.00 0.00 + I = 0.209523268 + 0.57 I = 0.209523268 + 0.57 Combine like terms: 0.209523268 + 0.57 = 0.779523268 I = 0.779523268 Simplifying I = 0.779523268

Subproblem 2

I + -0.57 = -0.209523268 Simplifying I + -0.57 = -0.209523268 Reorder the terms: -0.57 + I = -0.209523268 Solving -0.57 + I = -0.209523268 Solving for variable 'I'. Move all terms containing I to the left, all other terms to the right. Add '0.57' to each side of the equation. -0.57 + 0.57 + I = -0.209523268 + 0.57 Combine like terms: -0.57 + 0.57 = 0.00 0.00 + I = -0.209523268 + 0.57 I = -0.209523268 + 0.57 Combine like terms: -0.209523268 + 0.57 = 0.360476732 I = 0.360476732 Simplifying I = 0.360476732

Solution

The solution to the problem is based on the solutions from the subproblems. I = {0.779523268, 0.360476732}

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