x^2+x=216

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Solution for x^2+x=216 equation:


Simplifying
x2 + x = 216

Reorder the terms:
x + x2 = 216

Solving
x + x2 = 216

Solving for variable 'x'.

Reorder the terms:
-216 + x + x2 = 216 + -216

Combine like terms: 216 + -216 = 0
-216 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '216' to each side of the equation.
-216 + x + 216 + x2 = 0 + 216

Reorder the terms:
-216 + 216 + x + x2 = 0 + 216

Combine like terms: -216 + 216 = 0
0 + x + x2 = 0 + 216
x + x2 = 0 + 216

Combine like terms: 0 + 216 = 216
x + x2 = 216

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 = 216 + 0.25

Reorder the terms:
0.25 + x + x2 = 216 + 0.25

Combine like terms: 216 + 0.25 = 216.25
0.25 + x + x2 = 216.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(x + 0.5) equal to 14.70544117 and -14.70544117.

Subproblem 1

x + 0.5 = 14.70544117 Simplifying x + 0.5 = 14.70544117 Reorder the terms: 0.5 + x = 14.70544117 Solving 0.5 + x = 14.70544117 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 = 14.70544117 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.70544117 + -0.5 x = 14.70544117 + -0.5 Combine like terms: 14.70544117 + -0.5 = 14.20544117 x = 14.20544117 Simplifying x = 14.20544117

Subproblem 2

x + 0.5 = -14.70544117 Simplifying x + 0.5 = -14.70544117 Reorder the terms: 0.5 + x = -14.70544117 Solving 0.5 + x = -14.70544117 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 = -14.70544117 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.70544117 + -0.5 x = -14.70544117 + -0.5 Combine like terms: -14.70544117 + -0.5 = -15.20544117 x = -15.20544117 Simplifying x = -15.20544117

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.20544117, -15.20544117}

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