-0.2(x+5)(x+5)=0

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Solution for -0.2(x+5)(x+5)=0 equation:


Simplifying
-0.2(x + 5)(x + 5) = 0

Reorder the terms:
-0.2(5 + x)(x + 5) = 0

Reorder the terms:
-0.2(5 + x)(5 + x) = 0

Multiply (5 + x) * (5 + x)
-0.2(5(5 + x) + x(5 + x)) = 0
-0.2((5 * 5 + x * 5) + x(5 + x)) = 0
-0.2((25 + 5x) + x(5 + x)) = 0
-0.2(25 + 5x + (5 * x + x * x)) = 0
-0.2(25 + 5x + (5x + x2)) = 0

Combine like terms: 5x + 5x = 10x
-0.2(25 + 10x + x2) = 0
(25 * -0.2 + 10x * -0.2 + x2 * -0.2) = 0
(-5 + -2x + -0.2x2) = 0

Solving
-5 + -2x + -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'.
25 + 10x + x2 = 0

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 10x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 10x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 10x + x2 = 0 + -25
10x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
10x + x2 = -25

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -25 + 25

Reorder the terms:
25 + 10x + x2 = -25 + 25

Combine like terms: -25 + 25 = 0
25 + 10x + x2 = 0

Factor a perfect square on the left side:
(x + 5)(x + 5) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + 5) equal to 0 and 0.

Subproblem 1

x + 5 = 0 Simplifying x + 5 = 0 Reorder the terms: 5 + x = 0 Solving 5 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Subproblem 2

x + 5 = 0 Simplifying x + 5 = 0 Reorder the terms: 5 + x = 0 Solving 5 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5, -5}

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