0.2x^2+1x-20=0

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Solution for 0.2x^2+1x-20=0 equation:


Simplifying
0.2x2 + 1x + -20 = 0

Reorder the terms:
-20 + 1x + 0.2x2 = 0

Solving
-20 + 1x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
-100 + 5x + x2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 5x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 5x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 5x + x2 = 0 + 100
5x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
5x + x2 = 100

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 100 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 100 + 6.25

Combine like terms: 100 + 6.25 = 106.25
6.25 + 5x + x2 = 106.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.307764064 and -10.307764064.

Subproblem 1

x + 2.5 = 10.307764064 Simplifying x + 2.5 = 10.307764064 Reorder the terms: 2.5 + x = 10.307764064 Solving 2.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.307764064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.307764064 + -2.5 x = 10.307764064 + -2.5 Combine like terms: 10.307764064 + -2.5 = 7.807764064 x = 7.807764064 Simplifying x = 7.807764064

Subproblem 2

x + 2.5 = -10.307764064 Simplifying x + 2.5 = -10.307764064 Reorder the terms: 2.5 + x = -10.307764064 Solving 2.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.307764064 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.307764064 + -2.5 x = -10.307764064 + -2.5 Combine like terms: -10.307764064 + -2.5 = -12.807764064 x = -12.807764064 Simplifying x = -12.807764064

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.807764064, -12.807764064}

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