2.5x^2-4.75x+2.0=0

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Solution for 2.5x^2-4.75x+2.0=0 equation: 


Simplifying
2.5x2 + -4.75x + 2.0 = 0

Reorder the terms:
2.0 + -4.75x + 2.5x2 = 0

Solving
2.0 + -4.75x + 2.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.5'.
0.8 + -1.9x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -1.9x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -1.9x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -1.9x + x2 = 0 + -0.8
-1.9x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-1.9x + x2 = -0.8

The x term is -1.9x.  Take half its coefficient (-0.95).
Square it (0.9025) and add it to both sides.

Add '0.9025' to each side of the equation.
-1.9x + 0.9025 + x2 = -0.8 + 0.9025

Reorder the terms:
0.9025 + -1.9x + x2 = -0.8 + 0.9025

Combine like terms: -0.8 + 0.9025 = 0.1025
0.9025 + -1.9x + x2 = 0.1025

Factor a perfect square on the left side:
(x + -0.95)(x + -0.95) = 0.1025

Calculate the square root of the right side: 0.320156212

Break this problem into two subproblems by setting 
(x + -0.95) equal to 0.320156212 and -0.320156212.


Subproblem 1
x + -0.95 = 0.320156212

Simplifying
x + -0.95 = 0.320156212

Reorder the terms:
-0.95 + x = 0.320156212

Solving
-0.95 + x = 0.320156212

Solving for variable 'x'.

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

Add '0.95' to each side of the equation.
-0.95 + 0.95 + x = 0.320156212 + 0.95

Combine like terms: -0.95 + 0.95 = 0.00
0.00 + x = 0.320156212 + 0.95
x = 0.320156212 + 0.95

Combine like terms: 0.320156212 + 0.95 = 1.270156212
x = 1.270156212

Simplifying
x = 1.270156212


Subproblem 2
x + -0.95 = -0.320156212

Simplifying
x + -0.95 = -0.320156212

Reorder the terms:
-0.95 + x = -0.320156212

Solving
-0.95 + x = -0.320156212

Solving for variable 'x'.

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

Add '0.95' to each side of the equation.
-0.95 + 0.95 + x = -0.320156212 + 0.95

Combine like terms: -0.95 + 0.95 = 0.00
0.00 + x = -0.320156212 + 0.95
x = -0.320156212 + 0.95

Combine like terms: -0.320156212 + 0.95 = 0.629843788
x = 0.629843788

Simplifying
x = 0.629843788


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.270156212, 0.629843788}

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