(x)(x+1)+19=(x)+(x+1)

Solution for (x)(x+1)+19=(x)+(x+1) equation:

Simplifying
(x)(x + 1) + 19 = (x) + (x + 1)

Reorder the terms:
x(1 + x) + 19 = (x) + (x + 1)
(1 * x + x * x) + 19 = (x) + (x + 1)
(1x + x2) + 19 = (x) + (x + 1)

Reorder the terms:
19 + 1x + x2 = (x) + (x + 1)
19 + 1x + x2 = x + (x + 1)

Reorder the terms:
19 + 1x + x2 = x + (1 + x)

Remove parenthesis around (1 + x)
19 + 1x + x2 = x + 1 + x

Reorder the terms:
19 + 1x + x2 = 1 + x + x

Combine like terms: x + x = 2x
19 + 1x + x2 = 1 + 2x

Solving
19 + 1x + x2 = 1 + 2x

Solving for variable 'x'.

Reorder the terms:
19 + -1 + 1x + -2x + x2 = 1 + 2x + -1 + -2x

Combine like terms: 19 + -1 = 18
18 + 1x + -2x + x2 = 1 + 2x + -1 + -2x

Combine like terms: 1x + -2x = -1x
18 + -1x + x2 = 1 + 2x + -1 + -2x

Reorder the terms:
18 + -1x + x2 = 1 + -1 + 2x + -2x

Combine like terms: 1 + -1 = 0
18 + -1x + x2 = 0 + 2x + -2x
18 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
18 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -1x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -1x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x + x2 = 0 + -18
-1x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-1x + x2 = -18

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.
-1x + 0.25 + x2 = -18 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -18 + 0.25

Combine like terms: -18 + 0.25 = -17.75
0.25 + -1x + x2 = -17.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -17.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.