x^2-1.2x+0.16=0

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Solution for x^2-1.2x+0.16=0 equation:


Simplifying
x2 + -1.2x + 0.16 = 0

Reorder the terms:
0.16 + -1.2x + x2 = 0

Solving
0.16 + -1.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -1.2x + -0.16 + x2 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + -1.2x + x2 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -1.2x + x2 = 0 + -0.16
-1.2x + x2 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
-1.2x + x2 = -0.16

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 = -0.16 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -0.16 + 0.36

Combine like terms: -0.16 + 0.36 = 0.2
0.36 + -1.2x + x2 = 0.2

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.2

Calculate the square root of the right side: 0.447213596

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.447213596 and -0.447213596.

Subproblem 1

x + -0.6 = 0.447213596 Simplifying x + -0.6 = 0.447213596 Reorder the terms: -0.6 + x = 0.447213596 Solving -0.6 + x = 0.447213596 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 = 0.447213596 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.447213596 + 0.6 x = 0.447213596 + 0.6 Combine like terms: 0.447213596 + 0.6 = 1.047213596 x = 1.047213596 Simplifying x = 1.047213596

Subproblem 2

x + -0.6 = -0.447213596 Simplifying x + -0.6 = -0.447213596 Reorder the terms: -0.6 + x = -0.447213596 Solving -0.6 + x = -0.447213596 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 = -0.447213596 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.447213596 + 0.6 x = -0.447213596 + 0.6 Combine like terms: -0.447213596 + 0.6 = 0.152786404 x = 0.152786404 Simplifying x = 0.152786404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.047213596, 0.152786404}

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