x^2-4.26x+2.4=0

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Solution for x^2-4.26x+2.4=0 equation: 


Simplifying
x2 + -4.26x + 2.4 = 0

Reorder the terms:
2.4 + -4.26x + x2 = 0

Solving
2.4 + -4.26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -4.26x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -4.26x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -4.26x + x2 = 0 + -2.4
-4.26x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-4.26x + x2 = -2.4

The x term is -4.26x.  Take half its coefficient (-2.13).
Square it (4.5369) and add it to both sides.

Add '4.5369' to each side of the equation.
-4.26x + 4.5369 + x2 = -2.4 + 4.5369

Reorder the terms:
4.5369 + -4.26x + x2 = -2.4 + 4.5369

Combine like terms: -2.4 + 4.5369 = 2.1369
4.5369 + -4.26x + x2 = 2.1369

Factor a perfect square on the left side:
(x + -2.13)(x + -2.13) = 2.1369

Calculate the square root of the right side: 1.461813942

Break this problem into two subproblems by setting 
(x + -2.13) equal to 1.461813942 and -1.461813942.


Subproblem 1
x + -2.13 = 1.461813942

Simplifying
x + -2.13 = 1.461813942

Reorder the terms:
-2.13 + x = 1.461813942

Solving
-2.13 + x = 1.461813942

Solving for variable 'x'.

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

Add '2.13' to each side of the equation.
-2.13 + 2.13 + x = 1.461813942 + 2.13

Combine like terms: -2.13 + 2.13 = 0.00
0.00 + x = 1.461813942 + 2.13
x = 1.461813942 + 2.13

Combine like terms: 1.461813942 + 2.13 = 3.591813942
x = 3.591813942

Simplifying
x = 3.591813942


Subproblem 2
x + -2.13 = -1.461813942

Simplifying
x + -2.13 = -1.461813942

Reorder the terms:
-2.13 + x = -1.461813942

Solving
-2.13 + x = -1.461813942

Solving for variable 'x'.

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

Add '2.13' to each side of the equation.
-2.13 + 2.13 + x = -1.461813942 + 2.13

Combine like terms: -2.13 + 2.13 = 0.00
0.00 + x = -1.461813942 + 2.13
x = -1.461813942 + 2.13

Combine like terms: -1.461813942 + 2.13 = 0.668186058
x = 0.668186058

Simplifying
x = 0.668186058


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.591813942, 0.668186058}

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