0=-.004x^2+x+2.5

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Solution for 0=-.004x^2+x+2.5 equation:


Simplifying
0 = -0.004x2 + x + 2.5

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

Solving
0 = 2.5 + x + -0.004x2

Solving for variable 'x'.

Combine like terms: 0 + -2.5 = -2.5
-2.5 + -1x + 0.004x2 = 2.5 + x + -0.004x2 + -2.5 + -1x + 0.004x2

Reorder the terms:
-2.5 + -1x + 0.004x2 = 2.5 + -2.5 + x + -1x + -0.004x2 + 0.004x2

Combine like terms: 2.5 + -2.5 = 0.0
-2.5 + -1x + 0.004x2 = 0.0 + x + -1x + -0.004x2 + 0.004x2
-2.5 + -1x + 0.004x2 = x + -1x + -0.004x2 + 0.004x2

Combine like terms: x + -1x = 0
-2.5 + -1x + 0.004x2 = 0 + -0.004x2 + 0.004x2
-2.5 + -1x + 0.004x2 = -0.004x2 + 0.004x2

Combine like terms: -0.004x2 + 0.004x2 = 0.000
-2.5 + -1x + 0.004x2 = 0.000

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 -250x.  Take half its coefficient (-125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
-250x + 15625 + x2 = 625 + 15625

Reorder the terms:
15625 + -250x + x2 = 625 + 15625

Combine like terms: 625 + 15625 = 16250
15625 + -250x + x2 = 16250

Factor a perfect square on the left side:
(x + -125)(x + -125) = 16250

Calculate the square root of the right side: 127.47548784

Break this problem into two subproblems by setting 
(x + -125) equal to 127.47548784 and -127.47548784.

Subproblem 1

x + -125 = 127.47548784 Simplifying x + -125 = 127.47548784 Reorder the terms: -125 + x = 127.47548784 Solving -125 + x = 127.47548784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 127.47548784 + 125 Combine like terms: -125 + 125 = 0 0 + x = 127.47548784 + 125 x = 127.47548784 + 125 Combine like terms: 127.47548784 + 125 = 252.47548784 x = 252.47548784 Simplifying x = 252.47548784

Subproblem 2

x + -125 = -127.47548784 Simplifying x + -125 = -127.47548784 Reorder the terms: -125 + x = -127.47548784 Solving -125 + x = -127.47548784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -127.47548784 + 125 Combine like terms: -125 + 125 = 0 0 + x = -127.47548784 + 125 x = -127.47548784 + 125 Combine like terms: -127.47548784 + 125 = -2.47548784 x = -2.47548784 Simplifying x = -2.47548784

Solution

The solution to the problem is based on the solutions from the subproblems. x = {252.47548784, -2.47548784}

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