(x^2)+30x-2000=0

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Solution for (x^2)+30x-2000=0 equation: 


Simplifying
(x2) + 30x + -2000 = 0
x2 + 30x + -2000 = 0

Reorder the terms:
-2000 + 30x + x2 = 0

Solving
-2000 + 30x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + 30x + 2000 + x2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + 30x + x2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + 30x + x2 = 0 + 2000
30x + x2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
30x + x2 = 2000

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 2000 + 225

Reorder the terms:
225 + 30x + x2 = 2000 + 225

Combine like terms: 2000 + 225 = 2225
225 + 30x + x2 = 2225

Factor a perfect square on the left side:
(x + 15)(x + 15) = 2225

Calculate the square root of the right side: 47.16990566

Break this problem into two subproblems by setting 
(x + 15) equal to 47.16990566 and -47.16990566.


Subproblem 1
x + 15 = 47.16990566

Simplifying
x + 15 = 47.16990566

Reorder the terms:
15 + x = 47.16990566

Solving
15 + x = 47.16990566

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 47.16990566 + -15

Combine like terms: 15 + -15 = 0
0 + x = 47.16990566 + -15
x = 47.16990566 + -15

Combine like terms: 47.16990566 + -15 = 32.16990566
x = 32.16990566

Simplifying
x = 32.16990566


Subproblem 2
x + 15 = -47.16990566

Simplifying
x + 15 = -47.16990566

Reorder the terms:
15 + x = -47.16990566

Solving
15 + x = -47.16990566

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -47.16990566 + -15

Combine like terms: 15 + -15 = 0
0 + x = -47.16990566 + -15
x = -47.16990566 + -15

Combine like terms: -47.16990566 + -15 = -62.16990566
x = -62.16990566

Simplifying
x = -62.16990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.16990566, -62.16990566}

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