(x+5)*(x-2)=3000

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Solution for (x+5)*(x-2)=3000 equation: 


Simplifying
(x + 5)(x + -2) = 3000

Reorder the terms:
(5 + x)(x + -2) = 3000

Reorder the terms:
(5 + x)(-2 + x) = 3000

Multiply (5 + x) * (-2 + x)
(5(-2 + x) + x(-2 + x)) = 3000
((-2 * 5 + x * 5) + x(-2 + x)) = 3000
((-10 + 5x) + x(-2 + x)) = 3000
(-10 + 5x + (-2 * x + x * x)) = 3000
(-10 + 5x + (-2x + x2)) = 3000

Combine like terms: 5x + -2x = 3x
(-10 + 3x + x2) = 3000

Solving
-10 + 3x + x2 = 3000

Solving for variable 'x'.

Reorder the terms:
-10 + -3000 + 3x + x2 = 3000 + -3000

Combine like terms: -10 + -3000 = -3010
-3010 + 3x + x2 = 3000 + -3000

Combine like terms: 3000 + -3000 = 0
-3010 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3010' to each side of the equation.
-3010 + 3x + 3010 + x2 = 0 + 3010

Reorder the terms:
-3010 + 3010 + 3x + x2 = 0 + 3010

Combine like terms: -3010 + 3010 = 0
0 + 3x + x2 = 0 + 3010
3x + x2 = 0 + 3010

Combine like terms: 0 + 3010 = 3010
3x + x2 = 3010

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 = 3010 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 3010 + 2.25

Combine like terms: 3010 + 2.25 = 3012.25
2.25 + 3x + x2 = 3012.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3012.25

Calculate the square root of the right side: 54.883968515

Break this problem into two subproblems by setting 
(x + 1.5) equal to 54.883968515 and -54.883968515.


Subproblem 1
x + 1.5 = 54.883968515

Simplifying
x + 1.5 = 54.883968515

Reorder the terms:
1.5 + x = 54.883968515

Solving
1.5 + x = 54.883968515

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 = 54.883968515 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 54.883968515 + -1.5
x = 54.883968515 + -1.5

Combine like terms: 54.883968515 + -1.5 = 53.383968515
x = 53.383968515

Simplifying
x = 53.383968515


Subproblem 2
x + 1.5 = -54.883968515

Simplifying
x + 1.5 = -54.883968515

Reorder the terms:
1.5 + x = -54.883968515

Solving
1.5 + x = -54.883968515

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 = -54.883968515 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -54.883968515 + -1.5
x = -54.883968515 + -1.5

Combine like terms: -54.883968515 + -1.5 = -56.383968515
x = -56.383968515

Simplifying
x = -56.383968515


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.383968515, -56.383968515}

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