x*(x+1)=2147483647

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Solution for x*(x+1)=2147483647 equation:


Simplifying
x(x + 1) = 2147483647

Reorder the terms:
x(1 + x) = 2147483647
(1 * x + x * x) = 2147483647
(1x + x2) = 2147483647

Solving
1x + x2 = 2147483647

Solving for variable 'x'.

Reorder the terms:
-2147483647 + 1x + x2 = 2147483647 + -2147483647

Combine like terms: 2147483647 + -2147483647 = 0
-2147483647 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2147483647' to each side of the equation.
-2147483647 + 1x + 2147483647 + x2 = 0 + 2147483647

Reorder the terms:
-2147483647 + 2147483647 + 1x + x2 = 0 + 2147483647

Combine like terms: -2147483647 + 2147483647 = 0
0 + 1x + x2 = 0 + 2147483647
1x + x2 = 0 + 2147483647

Combine like terms: 0 + 2147483647 = 2147483647
1x + x2 = 2147483647

The x term is 1x.  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 = 2147483647 + 0.25

Reorder the terms:
0.25 + x + x2 = 2147483647 + 0.25

Combine like terms: 2147483647 + 0.25 = 2147483647.25
0.25 + x + x2 = 2147483647.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2147483647.25

Calculate the square root of the right side: 46340.950003749

Break this problem into two subproblems by setting 
(x + 0.5) equal to 46340.950003749 and -46340.950003749.

Subproblem 1

x + 0.5 = 46340.950003749 Simplifying x + 0.5 = 46340.950003749 Reorder the terms: 0.5 + x = 46340.950003749 Solving 0.5 + x = 46340.950003749 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 = 46340.950003749 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 46340.950003749 + -0.5 x = 46340.950003749 + -0.5 Combine like terms: 46340.950003749 + -0.5 = 46340.450003749 x = 46340.450003749 Simplifying x = 46340.450003749

Subproblem 2

x + 0.5 = -46340.950003749 Simplifying x + 0.5 = -46340.950003749 Reorder the terms: 0.5 + x = -46340.950003749 Solving 0.5 + x = -46340.950003749 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 = -46340.950003749 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -46340.950003749 + -0.5 x = -46340.950003749 + -0.5 Combine like terms: -46340.950003749 + -0.5 = -46341.450003749 x = -46341.450003749 Simplifying x = -46341.450003749

Solution

The solution to the problem is based on the solutions from the subproblems. x = {46340.450003749, -46341.450003749}

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