x^2-8.5x+3.75=0

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Solution for x^2-8.5x+3.75=0 equation: 


Simplifying
x2 + -8.5x + 3.75 = 0

Reorder the terms:
3.75 + -8.5x + x2 = 0

Solving
3.75 + -8.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -8.5x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -8.5x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -8.5x + x2 = 0 + -3.75
-8.5x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-8.5x + x2 = -3.75

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = -3.75 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = -3.75 + 18.0625

Combine like terms: -3.75 + 18.0625 = 14.3125
18.0625 + -8.5x + x2 = 14.3125

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 14.3125

Calculate the square root of the right side: 3.783186488

Break this problem into two subproblems by setting 
(x + -4.25) equal to 3.783186488 and -3.783186488.


Subproblem 1
x + -4.25 = 3.783186488

Simplifying
x + -4.25 = 3.783186488

Reorder the terms:
-4.25 + x = 3.783186488

Solving
-4.25 + x = 3.783186488

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = 3.783186488 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = 3.783186488 + 4.25
x = 3.783186488 + 4.25

Combine like terms: 3.783186488 + 4.25 = 8.033186488
x = 8.033186488

Simplifying
x = 8.033186488


Subproblem 2
x + -4.25 = -3.783186488

Simplifying
x + -4.25 = -3.783186488

Reorder the terms:
-4.25 + x = -3.783186488

Solving
-4.25 + x = -3.783186488

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = -3.783186488 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = -3.783186488 + 4.25
x = -3.783186488 + 4.25

Combine like terms: -3.783186488 + 4.25 = 0.466813512
x = 0.466813512

Simplifying
x = 0.466813512


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.033186488, 0.466813512}

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