(x-2)(x+7)=20

Solution for (x-2)(x+7)=20 equation:

Simplifying
(x + -2)(x + 7) = 20

Reorder the terms:
(-2 + x)(x + 7) = 20

Reorder the terms:
(-2 + x)(7 + x) = 20

Multiply (-2 + x) * (7 + x)
(-2(7 + x) + x(7 + x)) = 20
((7 * -2 + x * -2) + x(7 + x)) = 20
((-14 + -2x) + x(7 + x)) = 20
(-14 + -2x + (7 * x + x * x)) = 20
(-14 + -2x + (7x + x2)) = 20

Combine like terms: -2x + 7x = 5x
(-14 + 5x + x2) = 20

Solving
-14 + 5x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-14 + -20 + 5x + x2 = 20 + -20

Combine like terms: -14 + -20 = -34
-34 + 5x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-34 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 5x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + 5x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 5x + x2 = 0 + 34
5x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
5x + x2 = 34

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 = 34 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 34 + 6.25

Combine like terms: 34 + 6.25 = 40.25
6.25 + 5x + x2 = 40.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.34428877 and -6.34428877.

Subproblem 1
x + 2.5 = 6.34428877

Simplifying
x + 2.5 = 6.34428877

Reorder the terms:
2.5 + x = 6.34428877

Solving
2.5 + x = 6.34428877

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 = 6.34428877 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.34428877 + -2.5
x = 6.34428877 + -2.5

Combine like terms: 6.34428877 + -2.5 = 3.84428877
x = 3.84428877

Simplifying
x = 3.84428877

Subproblem 2
x + 2.5 = -6.34428877

Simplifying
x + 2.5 = -6.34428877

Reorder the terms:
2.5 + x = -6.34428877

Solving
2.5 + x = -6.34428877

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 = -6.34428877 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.34428877 + -2.5
x = -6.34428877 + -2.5

Combine like terms: -6.34428877 + -2.5 = -8.84428877
x = -8.84428877

Simplifying
x = -8.84428877

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.84428877, -8.84428877}