(x+2)(x-1)=6.75

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Solution for (x+2)(x-1)=6.75 equation: 


Simplifying
(x + 2)(x + -1) = 6.75

Reorder the terms:
(2 + x)(x + -1) = 6.75

Reorder the terms:
(2 + x)(-1 + x) = 6.75

Multiply (2 + x) * (-1 + x)
(2(-1 + x) + x(-1 + x)) = 6.75
((-1 * 2 + x * 2) + x(-1 + x)) = 6.75
((-2 + 2x) + x(-1 + x)) = 6.75
(-2 + 2x + (-1 * x + x * x)) = 6.75
(-2 + 2x + (-1x + x2)) = 6.75

Combine like terms: 2x + -1x = 1x
(-2 + 1x + x2) = 6.75

Solving
-2 + 1x + x2 = 6.75

Solving for variable 'x'.

Reorder the terms:
-2 + -6.75 + 1x + x2 = 6.75 + -6.75

Combine like terms: -2 + -6.75 = -8.75
-8.75 + 1x + x2 = 6.75 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
-8.75 + 1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + 1x + 8.75 + x2 = 0.00 + 8.75

Reorder the terms:
-8.75 + 8.75 + 1x + x2 = 0.00 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + 1x + x2 = 0.00 + 8.75
1x + x2 = 0.00 + 8.75

Combine like terms: 0.00 + 8.75 = 8.75
1x + x2 = 8.75

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 8.75 + 0.25

Reorder the terms:
0.25 + x + x2 = 8.75 + 0.25

Combine like terms: 8.75 + 0.25 = 9
0.25 + x + x2 = 9

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3 and -3.


Subproblem 1
x + 0.5 = 3

Simplifying
x + 0.5 = 3

Reorder the terms:
0.5 + x = 3

Solving
0.5 + x = 3

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3 + -0.5
x = 3 + -0.5

Combine like terms: 3 + -0.5 = 2.5
x = 2.5

Simplifying
x = 2.5


Subproblem 2
x + 0.5 = -3

Simplifying
x + 0.5 = -3

Reorder the terms:
0.5 + x = -3

Solving
0.5 + x = -3

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3 + -0.5
x = -3 + -0.5

Combine like terms: -3 + -0.5 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5, -3.5}

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