4x^2-16x+2.5=0

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Solution for 4x^2-16x+2.5=0 equation: 


Simplifying
4x2 + -16x + 2.5 = 0

Reorder the terms:
2.5 + -16x + 4x2 = 0

Solving
2.5 + -16x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
0.625 + -4x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -4x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -4x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -4x + x2 = 0 + -0.625
-4x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-4x + x2 = -0.625

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -0.625 + 4

Reorder the terms:
4 + -4x + x2 = -0.625 + 4

Combine like terms: -0.625 + 4 = 3.375
4 + -4x + x2 = 3.375

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3.375

Calculate the square root of the right side: 1.837117307

Break this problem into two subproblems by setting 
(x + -2) equal to 1.837117307 and -1.837117307.


Subproblem 1
x + -2 = 1.837117307

Simplifying
x + -2 = 1.837117307

Reorder the terms:
-2 + x = 1.837117307

Solving
-2 + x = 1.837117307

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.837117307 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.837117307 + 2
x = 1.837117307 + 2

Combine like terms: 1.837117307 + 2 = 3.837117307
x = 3.837117307

Simplifying
x = 3.837117307


Subproblem 2
x + -2 = -1.837117307

Simplifying
x + -2 = -1.837117307

Reorder the terms:
-2 + x = -1.837117307

Solving
-2 + x = -1.837117307

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.837117307 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.837117307 + 2
x = -1.837117307 + 2

Combine like terms: -1.837117307 + 2 = 0.162882693
x = 0.162882693

Simplifying
x = 0.162882693


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.837117307, 0.162882693}

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