x^2-3.5x-1=0

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Solution for x^2-3.5x-1=0 equation: 


Simplifying
x2 + -3.5x + -1 = 0

Reorder the terms:
-1 + -3.5x + x2 = 0

Solving
-1 + -3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.5x + x2 = 0 + 1
-3.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.5x + x2 = 1

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 = 1 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 1 + 3.0625

Combine like terms: 1 + 3.0625 = 4.0625
3.0625 + -3.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.015564437 and -2.015564437.


Subproblem 1
x + -1.75 = 2.015564437

Simplifying
x + -1.75 = 2.015564437

Reorder the terms:
-1.75 + x = 2.015564437

Solving
-1.75 + x = 2.015564437

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 = 2.015564437 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.015564437 + 1.75
x = 2.015564437 + 1.75

Combine like terms: 2.015564437 + 1.75 = 3.765564437
x = 3.765564437

Simplifying
x = 3.765564437


Subproblem 2
x + -1.75 = -2.015564437

Simplifying
x + -1.75 = -2.015564437

Reorder the terms:
-1.75 + x = -2.015564437

Solving
-1.75 + x = -2.015564437

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 = -2.015564437 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.015564437 + 1.75
x = -2.015564437 + 1.75

Combine like terms: -2.015564437 + 1.75 = -0.265564437
x = -0.265564437

Simplifying
x = -0.265564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.765564437, -0.265564437}

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