x(x+1)=271

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Solution for x(x+1)=271 equation:


Simplifying
x(x + 1) = 271

Reorder the terms:
x(1 + x) = 271
(1 * x + x * x) = 271
(1x + x2) = 271

Solving
1x + x2 = 271

Solving for variable 'x'.

Reorder the terms:
-271 + 1x + x2 = 271 + -271

Combine like terms: 271 + -271 = 0
-271 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '271' to each side of the equation.
-271 + 1x + 271 + x2 = 0 + 271

Reorder the terms:
-271 + 271 + 1x + x2 = 0 + 271

Combine like terms: -271 + 271 = 0
0 + 1x + x2 = 0 + 271
1x + x2 = 0 + 271

Combine like terms: 0 + 271 = 271
1x + x2 = 271

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 = 271 + 0.25

Reorder the terms:
0.25 + x + x2 = 271 + 0.25

Combine like terms: 271 + 0.25 = 271.25
0.25 + x + x2 = 271.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 271.25

Calculate the square root of the right side: 16.469669092

Break this problem into two subproblems by setting 
(x + 0.5) equal to 16.469669092 and -16.469669092.

Subproblem 1

x + 0.5 = 16.469669092 Simplifying x + 0.5 = 16.469669092 Reorder the terms: 0.5 + x = 16.469669092 Solving 0.5 + x = 16.469669092 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 = 16.469669092 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.469669092 + -0.5 x = 16.469669092 + -0.5 Combine like terms: 16.469669092 + -0.5 = 15.969669092 x = 15.969669092 Simplifying x = 15.969669092

Subproblem 2

x + 0.5 = -16.469669092 Simplifying x + 0.5 = -16.469669092 Reorder the terms: 0.5 + x = -16.469669092 Solving 0.5 + x = -16.469669092 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 = -16.469669092 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.469669092 + -0.5 x = -16.469669092 + -0.5 Combine like terms: -16.469669092 + -0.5 = -16.969669092 x = -16.969669092 Simplifying x = -16.969669092

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.969669092, -16.969669092}

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