8631=40x-0.04x^2

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Solution for 8631=40x-0.04x^2 equation:


Simplifying
8631 = 40x + -0.04x2

Solving
8631 = 40x + -0.04x2

Solving for variable 'x'.

Reorder the terms:
8631 + -40x + 0.04x2 = 40x + -40x + -0.04x2 + 0.04x2

Combine like terms: 40x + -40x = 0
8631 + -40x + 0.04x2 = 0 + -0.04x2 + 0.04x2
8631 + -40x + 0.04x2 = -0.04x2 + 0.04x2

Combine like terms: -0.04x2 + 0.04x2 = 0.00
8631 + -40x + 0.04x2 = 0.00

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

Divide each side by '0.04'.
215775 + -1000x + x2 = 0

Move the constant term to the right:

Add '-215775' to each side of the equation.
215775 + -1000x + -215775 + x2 = 0 + -215775

Reorder the terms:
215775 + -215775 + -1000x + x2 = 0 + -215775

Combine like terms: 215775 + -215775 = 0
0 + -1000x + x2 = 0 + -215775
-1000x + x2 = 0 + -215775

Combine like terms: 0 + -215775 = -215775
-1000x + x2 = -215775

The x term is -1000x.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000x + 250000 + x2 = -215775 + 250000

Reorder the terms:
250000 + -1000x + x2 = -215775 + 250000

Combine like terms: -215775 + 250000 = 34225
250000 + -1000x + x2 = 34225

Factor a perfect square on the left side:
(x + -500)(x + -500) = 34225

Calculate the square root of the right side: 185

Break this problem into two subproblems by setting 
(x + -500) equal to 185 and -185.

Subproblem 1

x + -500 = 185 Simplifying x + -500 = 185 Reorder the terms: -500 + x = 185 Solving -500 + x = 185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 185 + 500 Combine like terms: -500 + 500 = 0 0 + x = 185 + 500 x = 185 + 500 Combine like terms: 185 + 500 = 685 x = 685 Simplifying x = 685

Subproblem 2

x + -500 = -185 Simplifying x + -500 = -185 Reorder the terms: -500 + x = -185 Solving -500 + x = -185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -185 + 500 Combine like terms: -500 + 500 = 0 0 + x = -185 + 500 x = -185 + 500 Combine like terms: -185 + 500 = 315 x = 315 Simplifying x = 315

Solution

The solution to the problem is based on the solutions from the subproblems. x = {685, 315}

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