x^2-708x-82800=0

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Solution for x^2-708x-82800=0 equation:


Simplifying
x2 + -708x + -82800 = 0

Reorder the terms:
-82800 + -708x + x2 = 0

Solving
-82800 + -708x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '82800' to each side of the equation.
-82800 + -708x + 82800 + x2 = 0 + 82800

Reorder the terms:
-82800 + 82800 + -708x + x2 = 0 + 82800

Combine like terms: -82800 + 82800 = 0
0 + -708x + x2 = 0 + 82800
-708x + x2 = 0 + 82800

Combine like terms: 0 + 82800 = 82800
-708x + x2 = 82800

The x term is -708x.  Take half its coefficient (-354).
Square it (125316) and add it to both sides.

Add '125316' to each side of the equation.
-708x + 125316 + x2 = 82800 + 125316

Reorder the terms:
125316 + -708x + x2 = 82800 + 125316

Combine like terms: 82800 + 125316 = 208116
125316 + -708x + x2 = 208116

Factor a perfect square on the left side:
(x + -354)(x + -354) = 208116

Calculate the square root of the right side: 456.197325726

Break this problem into two subproblems by setting 
(x + -354) equal to 456.197325726 and -456.197325726.

Subproblem 1

x + -354 = 456.197325726 Simplifying x + -354 = 456.197325726 Reorder the terms: -354 + x = 456.197325726 Solving -354 + x = 456.197325726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '354' to each side of the equation. -354 + 354 + x = 456.197325726 + 354 Combine like terms: -354 + 354 = 0 0 + x = 456.197325726 + 354 x = 456.197325726 + 354 Combine like terms: 456.197325726 + 354 = 810.197325726 x = 810.197325726 Simplifying x = 810.197325726

Subproblem 2

x + -354 = -456.197325726 Simplifying x + -354 = -456.197325726 Reorder the terms: -354 + x = -456.197325726 Solving -354 + x = -456.197325726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '354' to each side of the equation. -354 + 354 + x = -456.197325726 + 354 Combine like terms: -354 + 354 = 0 0 + x = -456.197325726 + 354 x = -456.197325726 + 354 Combine like terms: -456.197325726 + 354 = -102.197325726 x = -102.197325726 Simplifying x = -102.197325726

Solution

The solution to the problem is based on the solutions from the subproblems. x = {810.197325726, -102.197325726}

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