x^2-3x-1.75=0

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Solution for x^2-3x-1.75=0 equation: 


Simplifying
x2 + -3x + -1.75 = 0

Reorder the terms:
-1.75 + -3x + x2 = 0

Solving
-1.75 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -3x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -3x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -3x + x2 = 0 + 1.75
-3x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-3x + x2 = 1.75

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 1.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1.75 + 2.25

Combine like terms: 1.75 + 2.25 = 4
2.25 + -3x + x2 = 4

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2 and -2.


Subproblem 1
x + -1.5 = 2

Simplifying
x + -1.5 = 2

Reorder the terms:
-1.5 + x = 2

Solving
-1.5 + x = 2

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2 + 1.5
x = 2 + 1.5

Combine like terms: 2 + 1.5 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + -1.5 = -2

Simplifying
x + -1.5 = -2

Reorder the terms:
-1.5 + x = -2

Solving
-1.5 + x = -2

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2 + 1.5
x = -2 + 1.5

Combine like terms: -2 + 1.5 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, -0.5}

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