4000000x^2-280000x-5480000=0

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Solution for 4000000x^2-280000x-5480000=0 equation: 


Simplifying
4000000x2 + -280000x + -5480000 = 0

Reorder the terms:
-5480000 + -280000x + 4000000x2 = 0

Solving
-5480000 + -280000x + 4000000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '40000'.
40000(-137 + -7x + 100x2) = 0

Ignore the factor 40000.

Subproblem 1
Set the factor '(-137 + -7x + 100x2)' equal to zero and attempt to solve:

Simplifying
-137 + -7x + 100x2 = 0

Solving
-137 + -7x + 100x2 = 0

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

Divide each side by '100'.
-1.37 + -0.07x + x2 = 0.00

Move the constant term to the right:

Add '1.37' to each side of the equation.
-1.37 + -0.07x + 1.37 + x2 = 0.00 + 1.37

Reorder the terms:
-1.37 + 1.37 + -0.07x + x2 = 0.00 + 1.37

Combine like terms: -1.37 + 1.37 = 0.00
0.00 + -0.07x + x2 = 0.00 + 1.37
-0.07x + x2 = 0.00 + 1.37

Combine like terms: 0.00 + 1.37 = 1.37
-0.07x + x2 = 1.37

The x term is -0.07x.  Take half its coefficient (-0.035).
Square it (0.001225) and add it to both sides.

Add '0.001225' to each side of the equation.
-0.07x + 0.001225 + x2 = 1.37 + 0.001225

Reorder the terms:
0.001225 + -0.07x + x2 = 1.37 + 0.001225

Combine like terms: 1.37 + 0.001225 = 1.371225
0.001225 + -0.07x + x2 = 1.371225

Factor a perfect square on the left side:
(x + -0.035)(x + -0.035) = 1.371225

Calculate the square root of the right side: 1.170993168

Break this problem into two subproblems by setting 
(x + -0.035) equal to 1.170993168 and -1.170993168.


Subproblem 1
x + -0.035 = 1.170993168

Simplifying
x + -0.035 = 1.170993168

Reorder the terms:
-0.035 + x = 1.170993168

Solving
-0.035 + x = 1.170993168

Solving for variable 'x'.

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

Add '0.035' to each side of the equation.
-0.035 + 0.035 + x = 1.170993168 + 0.035

Combine like terms: -0.035 + 0.035 = 0.000
0.000 + x = 1.170993168 + 0.035
x = 1.170993168 + 0.035

Combine like terms: 1.170993168 + 0.035 = 1.205993168
x = 1.205993168

Simplifying
x = 1.205993168


Subproblem 2
x + -0.035 = -1.170993168

Simplifying
x + -0.035 = -1.170993168

Reorder the terms:
-0.035 + x = -1.170993168

Solving
-0.035 + x = -1.170993168

Solving for variable 'x'.

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

Add '0.035' to each side of the equation.
-0.035 + 0.035 + x = -1.170993168 + 0.035

Combine like terms: -0.035 + 0.035 = 0.000
0.000 + x = -1.170993168 + 0.035
x = -1.170993168 + 0.035

Combine like terms: -1.170993168 + 0.035 = -1.135993168
x = -1.135993168

Simplifying
x = -1.135993168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.205993168, -1.135993168}
Solution
x = {1.205993168, -1.135993168}

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