x^2+350x-5400=0

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Solution for x^2+350x-5400=0 equation: 


Simplifying
x2 + 350x + -5400 = 0

Reorder the terms:
-5400 + 350x + x2 = 0

Solving
-5400 + 350x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5400' to each side of the equation.
-5400 + 350x + 5400 + x2 = 0 + 5400

Reorder the terms:
-5400 + 5400 + 350x + x2 = 0 + 5400

Combine like terms: -5400 + 5400 = 0
0 + 350x + x2 = 0 + 5400
350x + x2 = 0 + 5400

Combine like terms: 0 + 5400 = 5400
350x + x2 = 5400

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 = 5400 + 30625

Reorder the terms:
30625 + 350x + x2 = 5400 + 30625

Combine like terms: 5400 + 30625 = 36025
30625 + 350x + x2 = 36025

Factor a perfect square on the left side:
(x + 175)(x + 175) = 36025

Calculate the square root of the right side: 189.802528961

Break this problem into two subproblems by setting 
(x + 175) equal to 189.802528961 and -189.802528961.


Subproblem 1
x + 175 = 189.802528961

Simplifying
x + 175 = 189.802528961

Reorder the terms:
175 + x = 189.802528961

Solving
175 + x = 189.802528961

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 = 189.802528961 + -175

Combine like terms: 175 + -175 = 0
0 + x = 189.802528961 + -175
x = 189.802528961 + -175

Combine like terms: 189.802528961 + -175 = 14.802528961
x = 14.802528961

Simplifying
x = 14.802528961


Subproblem 2
x + 175 = -189.802528961

Simplifying
x + 175 = -189.802528961

Reorder the terms:
175 + x = -189.802528961

Solving
175 + x = -189.802528961

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 = -189.802528961 + -175

Combine like terms: 175 + -175 = 0
0 + x = -189.802528961 + -175
x = -189.802528961 + -175

Combine like terms: -189.802528961 + -175 = -364.802528961
x = -364.802528961

Simplifying
x = -364.802528961


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.802528961, -364.802528961}

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