x^2+2x(0.4)=0.84

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Solution for x^2+2x(0.4)=0.84 equation: 


Simplifying
x2 + 2x(0.4) = 0.84

Reorder the terms for easier multiplication:
x2 + 2 * 0.4x = 0.84

Multiply 2 * 0.4
x2 + 0.8x = 0.84

Reorder the terms:
0.8x + x2 = 0.84

Solving
0.8x + x2 = 0.84

Solving for variable 'x'.

Reorder the terms:
-0.84 + 0.8x + x2 = 0.84 + -0.84

Combine like terms: 0.84 + -0.84 = 0.00
-0.84 + 0.8x + 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 + 0.8x + 0.84 + x2 = 0.00 + 0.84

Reorder the terms:
-0.84 + 0.84 + 0.8x + x2 = 0.00 + 0.84

Combine like terms: -0.84 + 0.84 = 0.00
0.00 + 0.8x + x2 = 0.00 + 0.84
0.8x + x2 = 0.00 + 0.84

Combine like terms: 0.00 + 0.84 = 0.84
0.8x + x2 = 0.84

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 0.84 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 0.84 + 0.16

Combine like terms: 0.84 + 0.16 = 1
0.16 + 0.8x + x2 = 1

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1 and -1.


Subproblem 1
x + 0.4 = 1

Simplifying
x + 0.4 = 1

Reorder the terms:
0.4 + x = 1

Solving
0.4 + x = 1

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1 + -0.4
x = 1 + -0.4

Combine like terms: 1 + -0.4 = 0.6
x = 0.6

Simplifying
x = 0.6


Subproblem 2
x + 0.4 = -1

Simplifying
x + 0.4 = -1

Reorder the terms:
0.4 + x = -1

Solving
0.4 + x = -1

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1 + -0.4
x = -1 + -0.4

Combine like terms: -1 + -0.4 = -1.4
x = -1.4

Simplifying
x = -1.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6, -1.4}

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