0.2x^2+4x-6=0

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Solution for 0.2x^2+4x-6=0 equation:


Simplifying
0.2x2 + 4x + -6 = 0

Reorder the terms:
-6 + 4x + 0.2x2 = 0

Solving
-6 + 4x + 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'.
-30 + 20x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 20x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 20x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 20x + x2 = 0 + 30
20x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
20x + x2 = 30

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 30 + 100

Reorder the terms:
100 + 20x + x2 = 30 + 100

Combine like terms: 30 + 100 = 130
100 + 20x + x2 = 130

Factor a perfect square on the left side:
(x + 10)(x + 10) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(x + 10) equal to 11.401754251 and -11.401754251.

Subproblem 1

x + 10 = 11.401754251 Simplifying x + 10 = 11.401754251 Reorder the terms: 10 + x = 11.401754251 Solving 10 + x = 11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.401754251 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.401754251 + -10 x = 11.401754251 + -10 Combine like terms: 11.401754251 + -10 = 1.401754251 x = 1.401754251 Simplifying x = 1.401754251

Subproblem 2

x + 10 = -11.401754251 Simplifying x + 10 = -11.401754251 Reorder the terms: 10 + x = -11.401754251 Solving 10 + x = -11.401754251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.401754251 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.401754251 + -10 x = -11.401754251 + -10 Combine like terms: -11.401754251 + -10 = -21.401754251 x = -21.401754251 Simplifying x = -21.401754251

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.401754251, -21.401754251}

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