x^2+100x-6000=0

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Solution for x^2+100x-6000=0 equation:


Simplifying
x2 + 100x + -6000 = 0

Reorder the terms:
-6000 + 100x + x2 = 0

Solving
-6000 + 100x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6000' to each side of the equation.
-6000 + 100x + 6000 + x2 = 0 + 6000

Reorder the terms:
-6000 + 6000 + 100x + x2 = 0 + 6000

Combine like terms: -6000 + 6000 = 0
0 + 100x + x2 = 0 + 6000
100x + x2 = 0 + 6000

Combine like terms: 0 + 6000 = 6000
100x + x2 = 6000

The x term is 100x.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100x + 2500 + x2 = 6000 + 2500

Reorder the terms:
2500 + 100x + x2 = 6000 + 2500

Combine like terms: 6000 + 2500 = 8500
2500 + 100x + x2 = 8500

Factor a perfect square on the left side:
(x + 50)(x + 50) = 8500

Calculate the square root of the right side: 92.195444573

Break this problem into two subproblems by setting 
(x + 50) equal to 92.195444573 and -92.195444573.

Subproblem 1

x + 50 = 92.195444573 Simplifying x + 50 = 92.195444573 Reorder the terms: 50 + x = 92.195444573 Solving 50 + x = 92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 92.195444573 + -50 Combine like terms: 50 + -50 = 0 0 + x = 92.195444573 + -50 x = 92.195444573 + -50 Combine like terms: 92.195444573 + -50 = 42.195444573 x = 42.195444573 Simplifying x = 42.195444573

Subproblem 2

x + 50 = -92.195444573 Simplifying x + 50 = -92.195444573 Reorder the terms: 50 + x = -92.195444573 Solving 50 + x = -92.195444573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -92.195444573 + -50 Combine like terms: 50 + -50 = 0 0 + x = -92.195444573 + -50 x = -92.195444573 + -50 Combine like terms: -92.195444573 + -50 = -142.195444573 x = -142.195444573 Simplifying x = -142.195444573

Solution

The solution to the problem is based on the solutions from the subproblems. x = {42.195444573, -142.195444573}

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