x^2+x=65536

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Solution for x^2+x=65536 equation:


Simplifying
x2 + x = 65536

Reorder the terms:
x + x2 = 65536

Solving
x + x2 = 65536

Solving for variable 'x'.

Reorder the terms:
-65536 + x + x2 = 65536 + -65536

Combine like terms: 65536 + -65536 = 0
-65536 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '65536' to each side of the equation.
-65536 + x + 65536 + x2 = 0 + 65536

Reorder the terms:
-65536 + 65536 + x + x2 = 0 + 65536

Combine like terms: -65536 + 65536 = 0
0 + x + x2 = 0 + 65536
x + x2 = 0 + 65536

Combine like terms: 0 + 65536 = 65536
x + x2 = 65536

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 65536 + 0.25

Reorder the terms:
0.25 + x + x2 = 65536 + 0.25

Combine like terms: 65536 + 0.25 = 65536.25
0.25 + x + x2 = 65536.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 65536.25

Calculate the square root of the right side: 256.000488281

Break this problem into two subproblems by setting 
(x + 0.5) equal to 256.000488281 and -256.000488281.

Subproblem 1

x + 0.5 = 256.000488281 Simplifying x + 0.5 = 256.000488281 Reorder the terms: 0.5 + x = 256.000488281 Solving 0.5 + x = 256.000488281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 256.000488281 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 256.000488281 + -0.5 x = 256.000488281 + -0.5 Combine like terms: 256.000488281 + -0.5 = 255.500488281 x = 255.500488281 Simplifying x = 255.500488281

Subproblem 2

x + 0.5 = -256.000488281 Simplifying x + 0.5 = -256.000488281 Reorder the terms: 0.5 + x = -256.000488281 Solving 0.5 + x = -256.000488281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -256.000488281 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -256.000488281 + -0.5 x = -256.000488281 + -0.5 Combine like terms: -256.000488281 + -0.5 = -256.500488281 x = -256.500488281 Simplifying x = -256.500488281

Solution

The solution to the problem is based on the solutions from the subproblems. x = {255.500488281, -256.500488281}

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