3.75=x(x+1)

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Solution for 3.75=x(x+1) equation: 


Simplifying
3.75 = x(x + 1)

Reorder the terms:
3.75 = x(1 + x)
3.75 = (1 * x + x * x)
3.75 = (1x + x2)

Solving
3.75 = 1x + x2

Solving for variable 'x'.

Reorder the terms:
3.75 + -1x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
3.75 + -1x + -1x2 = 0 + x2 + -1x2
3.75 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3.75 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3.75 + x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x + x2 = 0 + 3.75
x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
x + x2 = 3.75

The x term is x.  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.
 + 0.25 + x2 = 3.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 3.75 + 0.25

Combine like terms: 3.75 + 0.25 = 4
1.25 + x2 = 4

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2 and -2.


Subproblem 1
x + 0.5 = 2

Simplifying
x + 0.5 = 2

Reorder the terms:
0.5 + x = 2

Solving
0.5 + x = 2

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 = 2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2 + -0.5
x = 2 + -0.5

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

Simplifying
x = 1.5


Subproblem 2
x + 0.5 = -2

Simplifying
x + 0.5 = -2

Reorder the terms:
0.5 + x = -2

Solving
0.5 + x = -2

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 = -2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2 + -0.5
x = -2 + -0.5

Combine like terms: -2 + -0.5 = -2.5
x = -2.5

Simplifying
x = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -2.5}

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