(x-2)(x+5)+5=33

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Solution for (x-2)(x+5)+5=33 equation: 


Simplifying
(x + -2)(x + 5) + 5 = 33

Reorder the terms:
(-2 + x)(x + 5) + 5 = 33

Reorder the terms:
(-2 + x)(5 + x) + 5 = 33

Multiply (-2 + x) * (5 + x)
(-2(5 + x) + x(5 + x)) + 5 = 33
((5 * -2 + x * -2) + x(5 + x)) + 5 = 33
((-10 + -2x) + x(5 + x)) + 5 = 33
(-10 + -2x + (5 * x + x * x)) + 5 = 33
(-10 + -2x + (5x + x2)) + 5 = 33

Combine like terms: -2x + 5x = 3x
(-10 + 3x + x2) + 5 = 33

Reorder the terms:
-10 + 5 + 3x + x2 = 33

Combine like terms: -10 + 5 = -5
-5 + 3x + x2 = 33

Solving
-5 + 3x + x2 = 33

Solving for variable 'x'.

Reorder the terms:
-5 + -33 + 3x + x2 = 33 + -33

Combine like terms: -5 + -33 = -38
-38 + 3x + x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-38 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + 3x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + 3x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 3x + x2 = 0 + 38
3x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
3x + x2 = 38

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 38 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 38 + 2.25

Combine like terms: 38 + 2.25 = 40.25
2.25 + 3x + x2 = 40.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + 1.5 = 6.34428877

Simplifying
x + 1.5 = 6.34428877

Reorder the terms:
1.5 + x = 6.34428877

Solving
1.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 6.34428877 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 6.34428877 + -1.5
x = 6.34428877 + -1.5

Combine like terms: 6.34428877 + -1.5 = 4.84428877
x = 4.84428877

Simplifying
x = 4.84428877


Subproblem 2
x + 1.5 = -6.34428877

Simplifying
x + 1.5 = -6.34428877

Reorder the terms:
1.5 + x = -6.34428877

Solving
1.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -6.34428877 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -6.34428877 + -1.5
x = -6.34428877 + -1.5

Combine like terms: -6.34428877 + -1.5 = -7.84428877
x = -7.84428877

Simplifying
x = -7.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.84428877, -7.84428877}

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