x^2+10x-6000=0

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Solution for x^2+10x-6000=0 equation:


Simplifying
x2 + 10x + -6000 = 0

Reorder the terms:
-6000 + 10x + x2 = 0

Solving
-6000 + 10x + 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 + 10x + 6000 + x2 = 0 + 6000

Reorder the terms:
-6000 + 6000 + 10x + x2 = 0 + 6000

Combine like terms: -6000 + 6000 = 0
0 + 10x + x2 = 0 + 6000
10x + x2 = 0 + 6000

Combine like terms: 0 + 6000 = 6000
10x + x2 = 6000

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 6000 + 25

Reorder the terms:
25 + 10x + x2 = 6000 + 25

Combine like terms: 6000 + 25 = 6025
25 + 10x + x2 = 6025

Factor a perfect square on the left side:
(x + 5)(x + 5) = 6025

Calculate the square root of the right side: 77.620873481

Break this problem into two subproblems by setting 
(x + 5) equal to 77.620873481 and -77.620873481.

Subproblem 1

x + 5 = 77.620873481 Simplifying x + 5 = 77.620873481 Reorder the terms: 5 + x = 77.620873481 Solving 5 + x = 77.620873481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 77.620873481 + -5 Combine like terms: 5 + -5 = 0 0 + x = 77.620873481 + -5 x = 77.620873481 + -5 Combine like terms: 77.620873481 + -5 = 72.620873481 x = 72.620873481 Simplifying x = 72.620873481

Subproblem 2

x + 5 = -77.620873481 Simplifying x + 5 = -77.620873481 Reorder the terms: 5 + x = -77.620873481 Solving 5 + x = -77.620873481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -77.620873481 + -5 Combine like terms: 5 + -5 = 0 0 + x = -77.620873481 + -5 x = -77.620873481 + -5 Combine like terms: -77.620873481 + -5 = -82.620873481 x = -82.620873481 Simplifying x = -82.620873481

Solution

The solution to the problem is based on the solutions from the subproblems. x = {72.620873481, -82.620873481}

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