x^2-2.4x+1.44=3.64

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Solution for x^2-2.4x+1.44=3.64 equation:


Simplifying
x2 + -2.4x + 1.44 = 3.64

Reorder the terms:
1.44 + -2.4x + x2 = 3.64

Solving
1.44 + -2.4x + x2 = 3.64

Solving for variable 'x'.

Reorder the terms:
1.44 + -3.64 + -2.4x + x2 = 3.64 + -3.64

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

Combine like terms: 3.64 + -3.64 = 0.00
-2.2 + -2.4x + x2 = 0.00

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 = 0.00 + 2.2

Reorder the terms:
-2.2 + 2.2 + -2.4x + x2 = 0.00 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -2.4x + x2 = 0.00 + 2.2
-2.4x + x2 = 0.00 + 2.2

Combine like terms: 0.00 + 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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