-0.004x^2+x+2.5=0

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Solution for -0.004x^2+x+2.5=0 equation: 


Simplifying
-0.004x2 + x + 2.5 = 0

Reorder the terms:
2.5 + x + -0.004x2 = 0

Solving
2.5 + x + -0.004x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.004 the coefficient of the squared term: 

Divide each side by '-0.004'.
-625 + -250x + x2 = 0

Move the constant term to the right:

Add '625' to each side of the equation.
-625 + -250x + 625 + x2 = 0 + 625

Reorder the terms:
-625 + 625 + -250x + x2 = 0 + 625

Combine like terms: -625 + 625 = 0
0 + -250x + x2 = 0 + 625
-250x + x2 = 0 + 625

Combine like terms: 0 + 625 = 625
-250x + x2 = 625

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-250x + 0.25 + x2 = 625 + 0.25

Reorder the terms:
0.25 + -250x + x2 = 625 + 0.25

Combine like terms: 625 + 0.25 = 625.25
0.25 + -250x + x2 = 625.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 625.25

Calculate the square root of the right side: 25.0049995

Break this problem into two subproblems by setting 
(x + 0.5) equal to 25.0049995 and -25.0049995.


Subproblem 1
x + 0.5 = 25.0049995

Simplifying
x + 0.5 = 25.0049995

Reorder the terms:
0.5 + x = 25.0049995

Solving
0.5 + x = 25.0049995

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 25.0049995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 25.0049995 + -0.5
x = 25.0049995 + -0.5

Combine like terms: 25.0049995 + -0.5 = 24.5049995
x = 24.5049995

Simplifying
x = 24.5049995


Subproblem 2
x + 0.5 = -25.0049995

Simplifying
x + 0.5 = -25.0049995

Reorder the terms:
0.5 + x = -25.0049995

Solving
0.5 + x = -25.0049995

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -25.0049995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -25.0049995 + -0.5
x = -25.0049995 + -0.5

Combine like terms: -25.0049995 + -0.5 = -25.5049995
x = -25.5049995

Simplifying
x = -25.5049995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.5049995, -25.5049995}

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