1.2x+x^2=.64

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Solution for 1.2x+x^2=.64 equation: 


Simplifying
1.2x + x2 = 0.64

Solving
1.2x + x2 = 0.64

Solving for variable 'x'.

Reorder the terms:
-0.64 + 1.2x + x2 = 0.64 + -0.64

Combine like terms: 0.64 + -0.64 = 0.00
-0.64 + 1.2x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.64' to each side of the equation.
-0.64 + 1.2x + 0.64 + x2 = 0.00 + 0.64

Reorder the terms:
-0.64 + 0.64 + 1.2x + x2 = 0.00 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
0.00 + 1.2x + x2 = 0.00 + 0.64
1.2x + x2 = 0.00 + 0.64

Combine like terms: 0.00 + 0.64 = 0.64
1.2x + x2 = 0.64

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 0.64 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 0.64 + 0.36

Combine like terms: 0.64 + 0.36 = 1
0.36 + 1.2x + x2 = 1

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1 and -1.


Subproblem 1
x + 0.6 = 1

Simplifying
x + 0.6 = 1

Reorder the terms:
0.6 + x = 1

Solving
0.6 + x = 1

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = 1 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = 1 + -0.6
x = 1 + -0.6

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

Simplifying
x = 0.4


Subproblem 2
x + 0.6 = -1

Simplifying
x + 0.6 = -1

Reorder the terms:
0.6 + x = -1

Solving
0.6 + x = -1

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = -1 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = -1 + -0.6
x = -1 + -0.6

Combine like terms: -1 + -0.6 = -1.6
x = -1.6

Simplifying
x = -1.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4, -1.6}

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