x^2-7.5x+3.5=0

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Solution for x^2-7.5x+3.5=0 equation: 


Simplifying
x2 + -7.5x + 3.5 = 0

Reorder the terms:
3.5 + -7.5x + x2 = 0

Solving
3.5 + -7.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -7.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -7.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -7.5x + x2 = 0 + -3.5
-7.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-7.5x + x2 = -3.5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -3.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -3.5 + 14.0625

Combine like terms: -3.5 + 14.0625 = 10.5625
14.0625 + -7.5x + x2 = 10.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.25 and -3.25.


Subproblem 1
x + -3.75 = 3.25

Simplifying
x + -3.75 = 3.25

Reorder the terms:
-3.75 + x = 3.25

Solving
-3.75 + x = 3.25

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 3.25 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.25 + 3.75
x = 3.25 + 3.75

Combine like terms: 3.25 + 3.75 = 7
x = 7

Simplifying
x = 7


Subproblem 2
x + -3.75 = -3.25

Simplifying
x + -3.75 = -3.25

Reorder the terms:
-3.75 + x = -3.25

Solving
-3.75 + x = -3.25

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -3.25 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.25 + 3.75
x = -3.25 + 3.75

Combine like terms: -3.25 + 3.75 = 0.5
x = 0.5

Simplifying
x = 0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7, 0.5}

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