-.03x^2+4x+8400=0

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Solution for -.03x^2+4x+8400=0 equation: 


Simplifying
-0.03x2 + 4x + 8400 = 0

Reorder the terms:
8400 + 4x + -0.03x2 = 0

Solving
8400 + 4x + -0.03x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.03 the coefficient of the squared term: 

Divide each side by '-0.03'.
-280000 + -133.3333333x + x2 = 0

Move the constant term to the right:

Add '280000' to each side of the equation.
-280000 + -133.3333333x + 280000 + x2 = 0 + 280000

Reorder the terms:
-280000 + 280000 + -133.3333333x + x2 = 0 + 280000

Combine like terms: -280000 + 280000 = 0
0 + -133.3333333x + x2 = 0 + 280000
-133.3333333x + x2 = 0 + 280000

Combine like terms: 0 + 280000 = 280000
-133.3333333x + x2 = 280000

The x term is -133.3333333x.  Take half its coefficient (-66.66666665).
Square it (4444.444442) and add it to both sides.

Add '4444.444442' to each side of the equation.
-133.3333333x + 4444.444442 + x2 = 280000 + 4444.444442

Reorder the terms:
4444.444442 + -133.3333333x + x2 = 280000 + 4444.444442

Combine like terms: 280000 + 4444.444442 = 284444.444442
4444.444442 + -133.3333333x + x2 = 284444.444442

Factor a perfect square on the left side:
(x + -66.66666665)(x + -66.66666665) = 284444.444442

Calculate the square root of the right side: 533.333333331

Break this problem into two subproblems by setting 
(x + -66.66666665) equal to 533.333333331 and -533.333333331.


Subproblem 1
x + -66.66666665 = 533.333333331

Simplifying
x + -66.66666665 = 533.333333331

Reorder the terms:
-66.66666665 + x = 533.333333331

Solving
-66.66666665 + x = 533.333333331

Solving for variable 'x'.

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

Add '66.66666665' to each side of the equation.
-66.66666665 + 66.66666665 + x = 533.333333331 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + x = 533.333333331 + 66.66666665
x = 533.333333331 + 66.66666665

Combine like terms: 533.333333331 + 66.66666665 = 599.999999981
x = 599.999999981

Simplifying
x = 599.999999981


Subproblem 2
x + -66.66666665 = -533.333333331

Simplifying
x + -66.66666665 = -533.333333331

Reorder the terms:
-66.66666665 + x = -533.333333331

Solving
-66.66666665 + x = -533.333333331

Solving for variable 'x'.

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

Add '66.66666665' to each side of the equation.
-66.66666665 + 66.66666665 + x = -533.333333331 + 66.66666665

Combine like terms: -66.66666665 + 66.66666665 = 0.00000000
0.00000000 + x = -533.333333331 + 66.66666665
x = -533.333333331 + 66.66666665

Combine like terms: -533.333333331 + 66.66666665 = -466.666666681
x = -466.666666681

Simplifying
x = -466.666666681


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {599.999999981, -466.666666681}

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