x^2-57x-676=0

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Solution for x^2-57x-676=0 equation:


Simplifying
x2 + -57x + -676 = 0

Reorder the terms:
-676 + -57x + x2 = 0

Solving
-676 + -57x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '676' to each side of the equation.
-676 + -57x + 676 + x2 = 0 + 676

Reorder the terms:
-676 + 676 + -57x + x2 = 0 + 676

Combine like terms: -676 + 676 = 0
0 + -57x + x2 = 0 + 676
-57x + x2 = 0 + 676

Combine like terms: 0 + 676 = 676
-57x + x2 = 676

The x term is -57x.  Take half its coefficient (-28.5).
Square it (812.25) and add it to both sides.

Add '812.25' to each side of the equation.
-57x + 812.25 + x2 = 676 + 812.25

Reorder the terms:
812.25 + -57x + x2 = 676 + 812.25

Combine like terms: 676 + 812.25 = 1488.25
812.25 + -57x + x2 = 1488.25

Factor a perfect square on the left side:
(x + -28.5)(x + -28.5) = 1488.25

Calculate the square root of the right side: 38.577843382

Break this problem into two subproblems by setting 
(x + -28.5) equal to 38.577843382 and -38.577843382.

Subproblem 1

x + -28.5 = 38.577843382 Simplifying x + -28.5 = 38.577843382 Reorder the terms: -28.5 + x = 38.577843382 Solving -28.5 + x = 38.577843382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = 38.577843382 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = 38.577843382 + 28.5 x = 38.577843382 + 28.5 Combine like terms: 38.577843382 + 28.5 = 67.077843382 x = 67.077843382 Simplifying x = 67.077843382

Subproblem 2

x + -28.5 = -38.577843382 Simplifying x + -28.5 = -38.577843382 Reorder the terms: -28.5 + x = -38.577843382 Solving -28.5 + x = -38.577843382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = -38.577843382 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = -38.577843382 + 28.5 x = -38.577843382 + 28.5 Combine like terms: -38.577843382 + 28.5 = -10.077843382 x = -10.077843382 Simplifying x = -10.077843382

Solution

The solution to the problem is based on the solutions from the subproblems. x = {67.077843382, -10.077843382}

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