x^2+x-16384=0

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Solution for x^2+x-16384=0 equation:


Simplifying
x2 + x + -16384 = 0

Reorder the terms:
-16384 + x + x2 = 0

Solving
-16384 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16384' to each side of the equation.
-16384 + x + 16384 + x2 = 0 + 16384

Reorder the terms:
-16384 + 16384 + x + x2 = 0 + 16384

Combine like terms: -16384 + 16384 = 0
0 + x + x2 = 0 + 16384
x + x2 = 0 + 16384

Combine like terms: 0 + 16384 = 16384
x + x2 = 16384

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 = 16384 + 0.25

Reorder the terms:
0.25 + x + x2 = 16384 + 0.25

Combine like terms: 16384 + 0.25 = 16384.25
0.25 + x + x2 = 16384.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 16384.25

Calculate the square root of the right side: 128.000976559

Break this problem into two subproblems by setting 
(x + 0.5) equal to 128.000976559 and -128.000976559.

Subproblem 1

x + 0.5 = 128.000976559 Simplifying x + 0.5 = 128.000976559 Reorder the terms: 0.5 + x = 128.000976559 Solving 0.5 + x = 128.000976559 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 = 128.000976559 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 128.000976559 + -0.5 x = 128.000976559 + -0.5 Combine like terms: 128.000976559 + -0.5 = 127.500976559 x = 127.500976559 Simplifying x = 127.500976559

Subproblem 2

x + 0.5 = -128.000976559 Simplifying x + 0.5 = -128.000976559 Reorder the terms: 0.5 + x = -128.000976559 Solving 0.5 + x = -128.000976559 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 = -128.000976559 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -128.000976559 + -0.5 x = -128.000976559 + -0.5 Combine like terms: -128.000976559 + -0.5 = -128.500976559 x = -128.500976559 Simplifying x = -128.500976559

Solution

The solution to the problem is based on the solutions from the subproblems. x = {127.500976559, -128.500976559}

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