x^2+x-215=0

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Solution for x^2+x-215=0 equation:


Simplifying
x2 + x + -215 = 0

Reorder the terms:
-215 + x + x2 = 0

Solving
-215 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '215' to each side of the equation.
-215 + x + 215 + x2 = 0 + 215

Reorder the terms:
-215 + 215 + x + x2 = 0 + 215

Combine like terms: -215 + 215 = 0
0 + x + x2 = 0 + 215
x + x2 = 0 + 215

Combine like terms: 0 + 215 = 215
x + x2 = 215

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 = 215 + 0.25

Reorder the terms:
0.25 + x + x2 = 215 + 0.25

Combine like terms: 215 + 0.25 = 215.25
0.25 + x + x2 = 215.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 215.25

Calculate the square root of the right side: 14.671400751

Break this problem into two subproblems by setting 
(x + 0.5) equal to 14.671400751 and -14.671400751.

Subproblem 1

x + 0.5 = 14.671400751 Simplifying x + 0.5 = 14.671400751 Reorder the terms: 0.5 + x = 14.671400751 Solving 0.5 + x = 14.671400751 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 = 14.671400751 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.671400751 + -0.5 x = 14.671400751 + -0.5 Combine like terms: 14.671400751 + -0.5 = 14.171400751 x = 14.171400751 Simplifying x = 14.171400751

Subproblem 2

x + 0.5 = -14.671400751 Simplifying x + 0.5 = -14.671400751 Reorder the terms: 0.5 + x = -14.671400751 Solving 0.5 + x = -14.671400751 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 = -14.671400751 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.671400751 + -0.5 x = -14.671400751 + -0.5 Combine like terms: -14.671400751 + -0.5 = -15.171400751 x = -15.171400751 Simplifying x = -15.171400751

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.171400751, -15.171400751}

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