-0.8(x^2)+36x-202.5=0

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Solution for -0.8(x^2)+36x-202.5=0 equation:


Simplifying
-0.8(x2) + 36x + -202.5 = 0

Reorder the terms:
-202.5 + 36x + -0.8x2 = 0

Solving
-202.5 + 36x + -0.8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
253.125 + -45x + x2 = 0

Move the constant term to the right:

Add '-253.125' to each side of the equation.
253.125 + -45x + -253.125 + x2 = 0 + -253.125

Reorder the terms:
253.125 + -253.125 + -45x + x2 = 0 + -253.125

Combine like terms: 253.125 + -253.125 = 0.000
0.000 + -45x + x2 = 0 + -253.125
-45x + x2 = 0 + -253.125

Combine like terms: 0 + -253.125 = -253.125
-45x + x2 = -253.125

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 = -253.125 + 506.25

Reorder the terms:
506.25 + -45x + x2 = -253.125 + 506.25

Combine like terms: -253.125 + 506.25 = 253.125
506.25 + -45x + x2 = 253.125

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 253.125

Calculate the square root of the right side: 15.909902577

Break this problem into two subproblems by setting 
(x + -22.5) equal to 15.909902577 and -15.909902577.

Subproblem 1

x + -22.5 = 15.909902577 Simplifying x + -22.5 = 15.909902577 Reorder the terms: -22.5 + x = 15.909902577 Solving -22.5 + x = 15.909902577 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 = 15.909902577 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 15.909902577 + 22.5 x = 15.909902577 + 22.5 Combine like terms: 15.909902577 + 22.5 = 38.409902577 x = 38.409902577 Simplifying x = 38.409902577

Subproblem 2

x + -22.5 = -15.909902577 Simplifying x + -22.5 = -15.909902577 Reorder the terms: -22.5 + x = -15.909902577 Solving -22.5 + x = -15.909902577 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 = -15.909902577 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -15.909902577 + 22.5 x = -15.909902577 + 22.5 Combine like terms: -15.909902577 + 22.5 = 6.590097423 x = 6.590097423 Simplifying x = 6.590097423

Solution

The solution to the problem is based on the solutions from the subproblems. x = {38.409902577, 6.590097423}

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