5x^2+15x-10000=0

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Solution for 5x^2+15x-10000=0 equation: 


Simplifying
5x2 + 15x + -10000 = 0

Reorder the terms:
-10000 + 15x + 5x2 = 0

Solving
-10000 + 15x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2000 + 3x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2000 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-2000 + 3x + x2 = 0

Solving
-2000 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + 3x + 2000 + x2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + 3x + x2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + 3x + x2 = 0 + 2000
3x + x2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
3x + x2 = 2000

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 = 2000 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2000 + 2.25

Combine like terms: 2000 + 2.25 = 2002.25
2.25 + 3x + x2 = 2002.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2002.25

Calculate the square root of the right side: 44.746508244

Break this problem into two subproblems by setting 
(x + 1.5) equal to 44.746508244 and -44.746508244.


Subproblem 1
x + 1.5 = 44.746508244

Simplifying
x + 1.5 = 44.746508244

Reorder the terms:
1.5 + x = 44.746508244

Solving
1.5 + x = 44.746508244

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 = 44.746508244 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 44.746508244 + -1.5
x = 44.746508244 + -1.5

Combine like terms: 44.746508244 + -1.5 = 43.246508244
x = 43.246508244

Simplifying
x = 43.246508244


Subproblem 2
x + 1.5 = -44.746508244

Simplifying
x + 1.5 = -44.746508244

Reorder the terms:
1.5 + x = -44.746508244

Solving
1.5 + x = -44.746508244

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 = -44.746508244 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -44.746508244 + -1.5
x = -44.746508244 + -1.5

Combine like terms: -44.746508244 + -1.5 = -46.246508244
x = -46.246508244

Simplifying
x = -46.246508244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {43.246508244, -46.246508244}
Solution
x = {43.246508244, -46.246508244}

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