-.01x^2-x+40=.01x^2+2x+20

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Solution for -.01x^2-x+40=.01x^2+2x+20 equation:


Simplifying
-0.01x2 + -1x + 40 = 0.01x2 + 2x + 20

Reorder the terms:
40 + -1x + -0.01x2 = 0.01x2 + 2x + 20

Reorder the terms:
40 + -1x + -0.01x2 = 20 + 2x + 0.01x2

Solving
40 + -1x + -0.01x2 = 20 + 2x + 0.01x2

Solving for variable 'x'.

Reorder the terms:
40 + -20 + -1x + -2x + -0.01x2 + -0.01x2 = 20 + 2x + 0.01x2 + -20 + -2x + -0.01x2

Combine like terms: 40 + -20 = 20
20 + -1x + -2x + -0.01x2 + -0.01x2 = 20 + 2x + 0.01x2 + -20 + -2x + -0.01x2

Combine like terms: -1x + -2x = -3x
20 + -3x + -0.01x2 + -0.01x2 = 20 + 2x + 0.01x2 + -20 + -2x + -0.01x2

Combine like terms: -0.01x2 + -0.01x2 = -0.02x2
20 + -3x + -0.02x2 = 20 + 2x + 0.01x2 + -20 + -2x + -0.01x2

Reorder the terms:
20 + -3x + -0.02x2 = 20 + -20 + 2x + -2x + 0.01x2 + -0.01x2

Combine like terms: 20 + -20 = 0
20 + -3x + -0.02x2 = 0 + 2x + -2x + 0.01x2 + -0.01x2
20 + -3x + -0.02x2 = 2x + -2x + 0.01x2 + -0.01x2

Combine like terms: 2x + -2x = 0
20 + -3x + -0.02x2 = 0 + 0.01x2 + -0.01x2
20 + -3x + -0.02x2 = 0.01x2 + -0.01x2

Combine like terms: 0.01x2 + -0.01x2 = 0.00
20 + -3x + -0.02x2 = 0.00

Begin completing the square.  Divide all terms by
-0.02 the coefficient of the squared term: 

Divide each side by '-0.02'.
-1000 + 150x + x2 = 0

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 150x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 150x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 150x + x2 = 0 + 1000
150x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
150x + x2 = 1000

The x term is 150x.  Take half its coefficient (75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
150x + 5625 + x2 = 1000 + 5625

Reorder the terms:
5625 + 150x + x2 = 1000 + 5625

Combine like terms: 1000 + 5625 = 6625
5625 + 150x + x2 = 6625

Factor a perfect square on the left side:
(x + 75)(x + 75) = 6625

Calculate the square root of the right side: 81.39410298

Break this problem into two subproblems by setting 
(x + 75) equal to 81.39410298 and -81.39410298.

Subproblem 1

x + 75 = 81.39410298 Simplifying x + 75 = 81.39410298 Reorder the terms: 75 + x = 81.39410298 Solving 75 + x = 81.39410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 81.39410298 + -75 Combine like terms: 75 + -75 = 0 0 + x = 81.39410298 + -75 x = 81.39410298 + -75 Combine like terms: 81.39410298 + -75 = 6.39410298 x = 6.39410298 Simplifying x = 6.39410298

Subproblem 2

x + 75 = -81.39410298 Simplifying x + 75 = -81.39410298 Reorder the terms: 75 + x = -81.39410298 Solving 75 + x = -81.39410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -81.39410298 + -75 Combine like terms: 75 + -75 = 0 0 + x = -81.39410298 + -75 x = -81.39410298 + -75 Combine like terms: -81.39410298 + -75 = -156.39410298 x = -156.39410298 Simplifying x = -156.39410298

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.39410298, -156.39410298}

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