x(x+1)=131

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Solution for x(x+1)=131 equation:


Simplifying
x(x + 1) = 131

Reorder the terms:
x(1 + x) = 131
(1 * x + x * x) = 131
(1x + x2) = 131

Solving
1x + x2 = 131

Solving for variable 'x'.

Reorder the terms:
-131 + 1x + x2 = 131 + -131

Combine like terms: 131 + -131 = 0
-131 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '131' to each side of the equation.
-131 + 1x + 131 + x2 = 0 + 131

Reorder the terms:
-131 + 131 + 1x + x2 = 0 + 131

Combine like terms: -131 + 131 = 0
0 + 1x + x2 = 0 + 131
1x + x2 = 0 + 131

Combine like terms: 0 + 131 = 131
1x + x2 = 131

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 = 131 + 0.25

Reorder the terms:
0.25 + x + x2 = 131 + 0.25

Combine like terms: 131 + 0.25 = 131.25
0.25 + x + x2 = 131.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 131.25

Calculate the square root of the right side: 11.456439237

Break this problem into two subproblems by setting 
(x + 0.5) equal to 11.456439237 and -11.456439237.

Subproblem 1

x + 0.5 = 11.456439237 Simplifying x + 0.5 = 11.456439237 Reorder the terms: 0.5 + x = 11.456439237 Solving 0.5 + x = 11.456439237 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 = 11.456439237 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.456439237 + -0.5 x = 11.456439237 + -0.5 Combine like terms: 11.456439237 + -0.5 = 10.956439237 x = 10.956439237 Simplifying x = 10.956439237

Subproblem 2

x + 0.5 = -11.456439237 Simplifying x + 0.5 = -11.456439237 Reorder the terms: 0.5 + x = -11.456439237 Solving 0.5 + x = -11.456439237 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 = -11.456439237 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.456439237 + -0.5 x = -11.456439237 + -0.5 Combine like terms: -11.456439237 + -0.5 = -11.956439237 x = -11.956439237 Simplifying x = -11.956439237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.956439237, -11.956439237}

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