2.0x^2-10.0x+5.4=0

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Solution for 2.0x^2-10.0x+5.4=0 equation:


Simplifying
2.0x2 + -10.0x + 5.4 = 0

Reorder the terms:
5.4 + -10.0x + 2.0x2 = 0

Solving
5.4 + -10.0x + 2.0x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2.0 the coefficient of the squared term: 

Divide each side by '2.0'.
2.7 + -5x + x2 = 0

Move the constant term to the right:

Add '-2.7' to each side of the equation.
2.7 + -5x + -2.7 + x2 = 0 + -2.7

Reorder the terms:
2.7 + -2.7 + -5x + x2 = 0 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + -5x + x2 = 0 + -2.7
-5x + x2 = 0 + -2.7

Combine like terms: 0 + -2.7 = -2.7
-5x + x2 = -2.7

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -2.7 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2.7 + 6.25

Combine like terms: -2.7 + 6.25 = 3.55
6.25 + -5x + x2 = 3.55

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.55

Calculate the square root of the right side: 1.884144368

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.884144368 and -1.884144368.


Subproblem 1
x + -2.5 = 1.884144368

Simplifying
x + -2.5 = 1.884144368

Reorder the terms:
-2.5 + x = 1.884144368

Solving
-2.5 + x = 1.884144368

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.884144368 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.884144368 + 2.5
x = 1.884144368 + 2.5

Combine like terms: 1.884144368 + 2.5 = 4.384144368
x = 4.384144368

Simplifying
x = 4.384144368


Subproblem 2
x + -2.5 = -1.884144368

Simplifying
x + -2.5 = -1.884144368

Reorder the terms:
-2.5 + x = -1.884144368

Solving
-2.5 + x = -1.884144368

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.884144368 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.884144368 + 2.5
x = -1.884144368 + 2.5

Combine like terms: -1.884144368 + 2.5 = 0.615855632
x = 0.615855632

Simplifying
x = 0.615855632


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.384144368, 0.615855632}

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