Simplifying
x2 + 82x + -2283 = 0
Reorder the terms:
-2283 + 82x + x2 = 0
Solving
-2283 + 82x + x2 = 0
Solving for variable 'x'.
Begin completing the square.
Move the constant term to the right:
Add '2283' to each side of the equation.
-2283 + 82x + 2283 + x2 = 0 + 2283
Reorder the terms:
-2283 + 2283 + 82x + x2 = 0 + 2283
Combine like terms: -2283 + 2283 = 0
0 + 82x + x2 = 0 + 2283
82x + x2 = 0 + 2283
Combine like terms: 0 + 2283 = 2283
82x + x2 = 2283
The x term is 82x. Take half its coefficient (41).
Square it (1681) and add it to both sides.
Add '1681' to each side of the equation.
82x + 1681 + x2 = 2283 + 1681
Reorder the terms:
1681 + 82x + x2 = 2283 + 1681
Combine like terms: 2283 + 1681 = 3964
1681 + 82x + x2 = 3964
Factor a perfect square on the left side:
(x + 41)(x + 41) = 3964
Calculate the square root of the right side: 62.960304955
Break this problem into two subproblems by setting
(x + 41) equal to 62.960304955 and -62.960304955.
Subproblem 1
x + 41 = 62.960304955
Simplifying
x + 41 = 62.960304955
Reorder the terms:
41 + x = 62.960304955
Solving
41 + x = 62.960304955
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-41' to each side of the equation.
41 + -41 + x = 62.960304955 + -41
Combine like terms: 41 + -41 = 0
0 + x = 62.960304955 + -41
x = 62.960304955 + -41
Combine like terms: 62.960304955 + -41 = 21.960304955
x = 21.960304955
Simplifying
x = 21.960304955
