x^2-2.4x-2.2=0

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Solution for x^2-2.4x-2.2=0 equation:


Simplifying
x2 + -2.4x + -2.2 = 0

Reorder the terms:
-2.2 + -2.4x + x2 = 0

Solving
-2.2 + -2.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -2.4x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -2.4x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -2.4x + x2 = 0 + 2.2
-2.4x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-2.4x + x2 = 2.2

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 2.2 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 2.2 + 1.44

Combine like terms: 2.2 + 1.44 = 3.64
1.44 + -2.4x + x2 = 3.64

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 3.64

Calculate the square root of the right side: 1.907878403

Break this problem into two subproblems by setting 
(x + -1.2) equal to 1.907878403 and -1.907878403.

Subproblem 1

x + -1.2 = 1.907878403 Simplifying x + -1.2 = 1.907878403 Reorder the terms: -1.2 + x = 1.907878403 Solving -1.2 + x = 1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.907878403 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.907878403 + 1.2 x = 1.907878403 + 1.2 Combine like terms: 1.907878403 + 1.2 = 3.107878403 x = 3.107878403 Simplifying x = 3.107878403

Subproblem 2

x + -1.2 = -1.907878403 Simplifying x + -1.2 = -1.907878403 Reorder the terms: -1.2 + x = -1.907878403 Solving -1.2 + x = -1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.907878403 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.907878403 + 1.2 x = -1.907878403 + 1.2 Combine like terms: -1.907878403 + 1.2 = -0.707878403 x = -0.707878403 Simplifying x = -0.707878403

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.107878403, -0.707878403}

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