x^2+80x+80=0

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


Simplifying
x2 + 80x + 80 = 0

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

Solving
80 + 80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -80 + 1600

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

Combine like terms: -80 + 1600 = 1520
1600 + 80x + x2 = 1520

Factor a perfect square on the left side:
(x + 40)(x + 40) = 1520

Calculate the square root of the right side: 38.987177379

Break this problem into two subproblems by setting 
(x + 40) equal to 38.987177379 and -38.987177379.

Subproblem 1

x + 40 = 38.987177379 Simplifying x + 40 = 38.987177379 Reorder the terms: 40 + x = 38.987177379 Solving 40 + x = 38.987177379 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 = 38.987177379 + -40 Combine like terms: 40 + -40 = 0 0 + x = 38.987177379 + -40 x = 38.987177379 + -40 Combine like terms: 38.987177379 + -40 = -1.012822621 x = -1.012822621 Simplifying x = -1.012822621

Subproblem 2

x + 40 = -38.987177379 Simplifying x + 40 = -38.987177379 Reorder the terms: 40 + x = -38.987177379 Solving 40 + x = -38.987177379 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 = -38.987177379 + -40 Combine like terms: 40 + -40 = 0 0 + x = -38.987177379 + -40 x = -38.987177379 + -40 Combine like terms: -38.987177379 + -40 = -78.987177379 x = -78.987177379 Simplifying x = -78.987177379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.012822621, -78.987177379}

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