x^2+11x=360

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Solution for x^2+11x=360 equation:


Simplifying
x2 + 11x = 360

Reorder the terms:
11x + x2 = 360

Solving
11x + x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 11x + x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + 11x + 360 + x2 = 0 + 360

Reorder the terms:
-360 + 360 + 11x + x2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + 11x + x2 = 0 + 360
11x + x2 = 0 + 360

Combine like terms: 0 + 360 = 360
11x + x2 = 360

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 360 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 360 + 30.25

Combine like terms: 360 + 30.25 = 390.25
30.25 + 11x + x2 = 390.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 390.25

Calculate the square root of the right side: 19.754746265

Break this problem into two subproblems by setting 
(x + 5.5) equal to 19.754746265 and -19.754746265.

Subproblem 1

x + 5.5 = 19.754746265 Simplifying x + 5.5 = 19.754746265 Reorder the terms: 5.5 + x = 19.754746265 Solving 5.5 + x = 19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 19.754746265 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 19.754746265 + -5.5 x = 19.754746265 + -5.5 Combine like terms: 19.754746265 + -5.5 = 14.254746265 x = 14.254746265 Simplifying x = 14.254746265

Subproblem 2

x + 5.5 = -19.754746265 Simplifying x + 5.5 = -19.754746265 Reorder the terms: 5.5 + x = -19.754746265 Solving 5.5 + x = -19.754746265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -19.754746265 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -19.754746265 + -5.5 x = -19.754746265 + -5.5 Combine like terms: -19.754746265 + -5.5 = -25.254746265 x = -25.254746265 Simplifying x = -25.254746265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.254746265, -25.254746265}

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