x^2+80x-3000=0

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Solution for x^2+80x-3000=0 equation:


Simplifying
x2 + 80x + -3000 = 0

Reorder the terms:
-3000 + 80x + x2 = 0

Solving
-3000 + 80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3000' to each side of the equation.
-3000 + 80x + 3000 + x2 = 0 + 3000

Reorder the terms:
-3000 + 3000 + 80x + x2 = 0 + 3000

Combine like terms: -3000 + 3000 = 0
0 + 80x + x2 = 0 + 3000
80x + x2 = 0 + 3000

Combine like terms: 0 + 3000 = 3000
80x + x2 = 3000

The x term is 80x.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80x + 1600 + x2 = 3000 + 1600

Reorder the terms:
1600 + 80x + x2 = 3000 + 1600

Combine like terms: 3000 + 1600 = 4600
1600 + 80x + x2 = 4600

Factor a perfect square on the left side:
(x + 40)(x + 40) = 4600

Calculate the square root of the right side: 67.823299831

Break this problem into two subproblems by setting 
(x + 40) equal to 67.823299831 and -67.823299831.

Subproblem 1

x + 40 = 67.823299831 Simplifying x + 40 = 67.823299831 Reorder the terms: 40 + x = 67.823299831 Solving 40 + x = 67.823299831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 67.823299831 + -40 Combine like terms: 40 + -40 = 0 0 + x = 67.823299831 + -40 x = 67.823299831 + -40 Combine like terms: 67.823299831 + -40 = 27.823299831 x = 27.823299831 Simplifying x = 27.823299831

Subproblem 2

x + 40 = -67.823299831 Simplifying x + 40 = -67.823299831 Reorder the terms: 40 + x = -67.823299831 Solving 40 + x = -67.823299831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -67.823299831 + -40 Combine like terms: 40 + -40 = 0 0 + x = -67.823299831 + -40 x = -67.823299831 + -40 Combine like terms: -67.823299831 + -40 = -107.823299831 x = -107.823299831 Simplifying x = -107.823299831

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.823299831, -107.823299831}

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