-9000x^2+6750x+506.25=0

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Solution for -9000x^2+6750x+506.25=0 equation: 


Simplifying
-9000x2 + 6750x + 506.25 = 0

Reorder the terms:
506.25 + 6750x + -9000x2 = 0

Solving
506.25 + 6750x + -9000x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-9000 the coefficient of the squared term: 

Divide each side by '-9000'.
-0.05625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.05625' to each side of the equation.
-0.05625 + -0.75x + 0.05625 + x2 = 0 + 0.05625

Reorder the terms:
-0.05625 + 0.05625 + -0.75x + x2 = 0 + 0.05625

Combine like terms: -0.05625 + 0.05625 = 0.00000
0.00000 + -0.75x + x2 = 0 + 0.05625
-0.75x + x2 = 0 + 0.05625

Combine like terms: 0 + 0.05625 = 0.05625
-0.75x + x2 = 0.05625

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.05625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.05625 + 0.140625

Combine like terms: 0.05625 + 0.140625 = 0.196875
0.140625 + -0.75x + x2 = 0.196875

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.196875

Calculate the square root of the right side: 0.443705984

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.443705984 and -0.443705984.


Subproblem 1
x + -0.375 = 0.443705984

Simplifying
x + -0.375 = 0.443705984

Reorder the terms:
-0.375 + x = 0.443705984

Solving
-0.375 + x = 0.443705984

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 0.443705984 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.443705984 + 0.375
x = 0.443705984 + 0.375

Combine like terms: 0.443705984 + 0.375 = 0.818705984
x = 0.818705984

Simplifying
x = 0.818705984


Subproblem 2
x + -0.375 = -0.443705984

Simplifying
x + -0.375 = -0.443705984

Reorder the terms:
-0.375 + x = -0.443705984

Solving
-0.375 + x = -0.443705984

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -0.443705984 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.443705984 + 0.375
x = -0.443705984 + 0.375

Combine like terms: -0.443705984 + 0.375 = -0.068705984
x = -0.068705984

Simplifying
x = -0.068705984


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.818705984, -0.068705984}

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