x^2-1.2x-1.2=0

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


Simplifying
x2 + -1.2x + -1.2 = 0

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

Solving
-1.2 + -1.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -1.2x + x2 = 0 + 1.2
-1.2x + x2 = 0 + 1.2

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

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 = 1.2 + 0.36

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

Combine like terms: 1.2 + 0.36 = 1.56
0.36 + -1.2x + x2 = 1.56

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 1.56

Calculate the square root of the right side: 1.2489996

Break this problem into two subproblems by setting 
(x + -0.6) equal to 1.2489996 and -1.2489996.

Subproblem 1

x + -0.6 = 1.2489996 Simplifying x + -0.6 = 1.2489996 Reorder the terms: -0.6 + x = 1.2489996 Solving -0.6 + x = 1.2489996 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 = 1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.2489996 + 0.6 x = 1.2489996 + 0.6 Combine like terms: 1.2489996 + 0.6 = 1.8489996 x = 1.8489996 Simplifying x = 1.8489996

Subproblem 2

x + -0.6 = -1.2489996 Simplifying x + -0.6 = -1.2489996 Reorder the terms: -0.6 + x = -1.2489996 Solving -0.6 + x = -1.2489996 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 = -1.2489996 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.2489996 + 0.6 x = -1.2489996 + 0.6 Combine like terms: -1.2489996 + 0.6 = -0.6489996 x = -0.6489996 Simplifying x = -0.6489996

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8489996, -0.6489996}

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