(x+7)(x-2)=104

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Solution for (x+7)(x-2)=104 equation: 


Simplifying
(x + 7)(x + -2) = 104

Reorder the terms:
(7 + x)(x + -2) = 104

Reorder the terms:
(7 + x)(-2 + x) = 104

Multiply (7 + x) * (-2 + x)
(7(-2 + x) + x(-2 + x)) = 104
((-2 * 7 + x * 7) + x(-2 + x)) = 104
((-14 + 7x) + x(-2 + x)) = 104
(-14 + 7x + (-2 * x + x * x)) = 104
(-14 + 7x + (-2x + x2)) = 104

Combine like terms: 7x + -2x = 5x
(-14 + 5x + x2) = 104

Solving
-14 + 5x + x2 = 104

Solving for variable 'x'.

Reorder the terms:
-14 + -104 + 5x + x2 = 104 + -104

Combine like terms: -14 + -104 = -118
-118 + 5x + x2 = 104 + -104

Combine like terms: 104 + -104 = 0
-118 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '118' to each side of the equation.
-118 + 5x + 118 + x2 = 0 + 118

Reorder the terms:
-118 + 118 + 5x + x2 = 0 + 118

Combine like terms: -118 + 118 = 0
0 + 5x + x2 = 0 + 118
5x + x2 = 0 + 118

Combine like terms: 0 + 118 = 118
5x + x2 = 118

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 118 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 118 + 6.25

Combine like terms: 118 + 6.25 = 124.25
6.25 + 5x + x2 = 124.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 124.25

Calculate the square root of the right side: 11.146748405

Break this problem into two subproblems by setting 
(x + 2.5) equal to 11.146748405 and -11.146748405.


Subproblem 1
x + 2.5 = 11.146748405

Simplifying
x + 2.5 = 11.146748405

Reorder the terms:
2.5 + x = 11.146748405

Solving
2.5 + x = 11.146748405

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 11.146748405 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 11.146748405 + -2.5
x = 11.146748405 + -2.5

Combine like terms: 11.146748405 + -2.5 = 8.646748405
x = 8.646748405

Simplifying
x = 8.646748405


Subproblem 2
x + 2.5 = -11.146748405

Simplifying
x + 2.5 = -11.146748405

Reorder the terms:
2.5 + x = -11.146748405

Solving
2.5 + x = -11.146748405

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -11.146748405 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -11.146748405 + -2.5
x = -11.146748405 + -2.5

Combine like terms: -11.146748405 + -2.5 = -13.646748405
x = -13.646748405

Simplifying
x = -13.646748405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.646748405, -13.646748405}

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