.02x^2+.5x-4=0

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Solution for .02x^2+.5x-4=0 equation:


Simplifying
0.02x2 + 0.5x + -4 = 0

Reorder the terms:
-4 + 0.5x + 0.02x2 = 0

Solving
-4 + 0.5x + 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'.
-200 + 25x + x2 = 0

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 25x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 25x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 25x + x2 = 0 + 200
25x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
25x + x2 = 200

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 200 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 200 + 156.25

Combine like terms: 200 + 156.25 = 356.25
156.25 + 25x + x2 = 356.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 356.25

Calculate the square root of the right side: 18.874586088

Break this problem into two subproblems by setting 
(x + 12.5) equal to 18.874586088 and -18.874586088.

Subproblem 1

x + 12.5 = 18.874586088 Simplifying x + 12.5 = 18.874586088 Reorder the terms: 12.5 + x = 18.874586088 Solving 12.5 + x = 18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 18.874586088 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 18.874586088 + -12.5 x = 18.874586088 + -12.5 Combine like terms: 18.874586088 + -12.5 = 6.374586088 x = 6.374586088 Simplifying x = 6.374586088

Subproblem 2

x + 12.5 = -18.874586088 Simplifying x + 12.5 = -18.874586088 Reorder the terms: 12.5 + x = -18.874586088 Solving 12.5 + x = -18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -18.874586088 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -18.874586088 + -12.5 x = -18.874586088 + -12.5 Combine like terms: -18.874586088 + -12.5 = -31.374586088 x = -31.374586088 Simplifying x = -31.374586088

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.374586088, -31.374586088}

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