x(x+0.4)=0.84

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Solution for x(x+0.4)=0.84 equation: 


Simplifying
x(x + 0.4) = 0.84

Reorder the terms:
x(0.4 + x) = 0.84
(0.4 * x + x * x) = 0.84
(0.4x + x2) = 0.84

Solving
0.4x + x2 = 0.84

Solving for variable 'x'.

Reorder the terms:
-0.84 + 0.4x + x2 = 0.84 + -0.84

Combine like terms: 0.84 + -0.84 = 0.00
-0.84 + 0.4x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.84' to each side of the equation.
-0.84 + 0.4x + 0.84 + x2 = 0.00 + 0.84

Reorder the terms:
-0.84 + 0.84 + 0.4x + x2 = 0.00 + 0.84

Combine like terms: -0.84 + 0.84 = 0.00
0.00 + 0.4x + x2 = 0.00 + 0.84
0.4x + x2 = 0.00 + 0.84

Combine like terms: 0.00 + 0.84 = 0.84
0.4x + x2 = 0.84

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 0.84 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 0.84 + 0.04

Combine like terms: 0.84 + 0.04 = 0.88
0.04 + 0.4x + x2 = 0.88

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 0.88

Calculate the square root of the right side: 0.938083152

Break this problem into two subproblems by setting 
(x + 0.2) equal to 0.938083152 and -0.938083152.


Subproblem 1
x + 0.2 = 0.938083152

Simplifying
x + 0.2 = 0.938083152

Reorder the terms:
0.2 + x = 0.938083152

Solving
0.2 + x = 0.938083152

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = 0.938083152 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = 0.938083152 + -0.2
x = 0.938083152 + -0.2

Combine like terms: 0.938083152 + -0.2 = 0.738083152
x = 0.738083152

Simplifying
x = 0.738083152


Subproblem 2
x + 0.2 = -0.938083152

Simplifying
x + 0.2 = -0.938083152

Reorder the terms:
0.2 + x = -0.938083152

Solving
0.2 + x = -0.938083152

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2' to each side of the equation.
0.2 + -0.2 + x = -0.938083152 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + x = -0.938083152 + -0.2
x = -0.938083152 + -0.2

Combine like terms: -0.938083152 + -0.2 = -1.138083152
x = -1.138083152

Simplifying
x = -1.138083152


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.738083152, -1.138083152}

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