x^2+350x-15000=0

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Solution for x^2+350x-15000=0 equation: 


Simplifying
x2 + 350x + -15000 = 0

Reorder the terms:
-15000 + 350x + x2 = 0

Solving
-15000 + 350x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '15000' to each side of the equation.
-15000 + 350x + 15000 + x2 = 0 + 15000

Reorder the terms:
-15000 + 15000 + 350x + x2 = 0 + 15000

Combine like terms: -15000 + 15000 = 0
0 + 350x + x2 = 0 + 15000
350x + x2 = 0 + 15000

Combine like terms: 0 + 15000 = 15000
350x + x2 = 15000

The x term is 350x.  Take half its coefficient (175).
Square it (30625) and add it to both sides.

Add '30625' to each side of the equation.
350x + 30625 + x2 = 15000 + 30625

Reorder the terms:
30625 + 350x + x2 = 15000 + 30625

Combine like terms: 15000 + 30625 = 45625
30625 + 350x + x2 = 45625

Factor a perfect square on the left side:
(x + 175)(x + 175) = 45625

Calculate the square root of the right side: 213.600093633

Break this problem into two subproblems by setting 
(x + 175) equal to 213.600093633 and -213.600093633.


Subproblem 1
x + 175 = 213.600093633

Simplifying
x + 175 = 213.600093633

Reorder the terms:
175 + x = 213.600093633

Solving
175 + x = 213.600093633

Solving for variable 'x'.

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

Add '-175' to each side of the equation.
175 + -175 + x = 213.600093633 + -175

Combine like terms: 175 + -175 = 0
0 + x = 213.600093633 + -175
x = 213.600093633 + -175

Combine like terms: 213.600093633 + -175 = 38.600093633
x = 38.600093633

Simplifying
x = 38.600093633


Subproblem 2
x + 175 = -213.600093633

Simplifying
x + 175 = -213.600093633

Reorder the terms:
175 + x = -213.600093633

Solving
175 + x = -213.600093633

Solving for variable 'x'.

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

Add '-175' to each side of the equation.
175 + -175 + x = -213.600093633 + -175

Combine like terms: 175 + -175 = 0
0 + x = -213.600093633 + -175
x = -213.600093633 + -175

Combine like terms: -213.600093633 + -175 = -388.600093633
x = -388.600093633

Simplifying
x = -388.600093633


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {38.600093633, -388.600093633}

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