-0.02x^2+0.9x+40=0

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Solution for -0.02x^2+0.9x+40=0 equation:


Simplifying
-0.02x2 + 0.9x + 40 = 0

Reorder the terms:
40 + 0.9x + -0.02x2 = 0

Solving
40 + 0.9x + -0.02x2 = 0

Solving for variable 'x'.

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

Divide each side by '-0.02'.
-2000 + -45x + x2 = 0

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + -45x + 2000 + x2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + -45x + x2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + -45x + x2 = 0 + 2000
-45x + x2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
-45x + x2 = 2000

The x term is -45x.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45x + 506.25 + x2 = 2000 + 506.25

Reorder the terms:
506.25 + -45x + x2 = 2000 + 506.25

Combine like terms: 2000 + 506.25 = 2506.25
506.25 + -45x + x2 = 2506.25

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 2506.25

Calculate the square root of the right side: 50.062460986

Break this problem into two subproblems by setting 
(x + -22.5) equal to 50.062460986 and -50.062460986.

Subproblem 1

x + -22.5 = 50.062460986 Simplifying x + -22.5 = 50.062460986 Reorder the terms: -22.5 + x = 50.062460986 Solving -22.5 + x = 50.062460986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 50.062460986 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 50.062460986 + 22.5 x = 50.062460986 + 22.5 Combine like terms: 50.062460986 + 22.5 = 72.562460986 x = 72.562460986 Simplifying x = 72.562460986

Subproblem 2

x + -22.5 = -50.062460986 Simplifying x + -22.5 = -50.062460986 Reorder the terms: -22.5 + x = -50.062460986 Solving -22.5 + x = -50.062460986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -50.062460986 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -50.062460986 + 22.5 x = -50.062460986 + 22.5 Combine like terms: -50.062460986 + 22.5 = -27.562460986 x = -27.562460986 Simplifying x = -27.562460986

Solution

The solution to the problem is based on the solutions from the subproblems. x = {72.562460986, -27.562460986}

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