x^2-3.5x-2=0

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


Simplifying
x2 + -3.5x + -2 = 0

Reorder the terms:
-2 + -3.5x + x2 = 0

Solving
-2 + -3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3.5x + x2 = 0 + 2
-3.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3.5x + x2 = 2

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 2 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 2 + 3.0625

Combine like terms: 2 + 3.0625 = 5.0625
3.0625 + -3.5x + x2 = 5.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.25 and -2.25.


Subproblem 1
x + -1.75 = 2.25

Simplifying
x + -1.75 = 2.25

Reorder the terms:
-1.75 + x = 2.25

Solving
-1.75 + x = 2.25

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 2.25 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.25 + 1.75
x = 2.25 + 1.75

Combine like terms: 2.25 + 1.75 = 4
x = 4

Simplifying
x = 4


Subproblem 2
x + -1.75 = -2.25

Simplifying
x + -1.75 = -2.25

Reorder the terms:
-1.75 + x = -2.25

Solving
-1.75 + x = -2.25

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -2.25 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.25 + 1.75
x = -2.25 + 1.75

Combine like terms: -2.25 + 1.75 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4, -0.5}

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