0=x^2+40x-6000

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Solution for 0=x^2+40x-6000 equation:


Simplifying
0 = x2 + 40x + -6000

Reorder the terms:
0 = -6000 + 40x + x2

Solving
0 = -6000 + 40x + x2

Solving for variable 'x'.

Combine like terms: 0 + 6000 = 6000
6000 + -40x + -1x2 = -6000 + 40x + x2 + 6000 + -40x + -1x2

Reorder the terms:
6000 + -40x + -1x2 = -6000 + 6000 + 40x + -40x + x2 + -1x2

Combine like terms: -6000 + 6000 = 0
6000 + -40x + -1x2 = 0 + 40x + -40x + x2 + -1x2
6000 + -40x + -1x2 = 40x + -40x + x2 + -1x2

Combine like terms: 40x + -40x = 0
6000 + -40x + -1x2 = 0 + x2 + -1x2
6000 + -40x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6000 + -40x + -1x2 = 0

Factor a trinomial.
(60 + -1x)(100 + x) = 0

Subproblem 1

Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60

Subproblem 2

Set the factor '(100 + x)' equal to zero and attempt to solve: Simplifying 100 + x = 0 Solving 100 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + x = 0 + -100 x = 0 + -100 Combine like terms: 0 + -100 = -100 x = -100 Simplifying x = -100

Solution

x = {60, -100}

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