92=84+19x+x^2

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Solution for 92=84+19x+x^2 equation: 


Simplifying
92 = 84 + 19x + x2

Solving
92 = 84 + 19x + x2

Solving for variable 'x'.

Combine like terms: 92 + -84 = 8
8 + -19x + -1x2 = 84 + 19x + x2 + -84 + -19x + -1x2

Reorder the terms:
8 + -19x + -1x2 = 84 + -84 + 19x + -19x + x2 + -1x2

Combine like terms: 84 + -84 = 0
8 + -19x + -1x2 = 0 + 19x + -19x + x2 + -1x2
8 + -19x + -1x2 = 19x + -19x + x2 + -1x2

Combine like terms: 19x + -19x = 0
8 + -19x + -1x2 = 0 + x2 + -1x2
8 + -19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -19x + -1x2 = 0

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

Divide each side by '-1'.
-8 + 19x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 19x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 19x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 19x + x2 = 0 + 8
19x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
19x + x2 = 8

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 8 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 8 + 90.25

Combine like terms: 8 + 90.25 = 98.25
90.25 + 19x + x2 = 98.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 98.25

Calculate the square root of the right side: 9.912113801

Break this problem into two subproblems by setting 
(x + 9.5) equal to 9.912113801 and -9.912113801.


Subproblem 1
x + 9.5 = 9.912113801

Simplifying
x + 9.5 = 9.912113801

Reorder the terms:
9.5 + x = 9.912113801

Solving
9.5 + x = 9.912113801

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 9.912113801 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 9.912113801 + -9.5
x = 9.912113801 + -9.5

Combine like terms: 9.912113801 + -9.5 = 0.412113801
x = 0.412113801

Simplifying
x = 0.412113801


Subproblem 2
x + 9.5 = -9.912113801

Simplifying
x + 9.5 = -9.912113801

Reorder the terms:
9.5 + x = -9.912113801

Solving
9.5 + x = -9.912113801

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -9.912113801 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -9.912113801 + -9.5
x = -9.912113801 + -9.5

Combine like terms: -9.912113801 + -9.5 = -19.412113801
x = -19.412113801

Simplifying
x = -19.412113801


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.412113801, -19.412113801}

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