x^2+17x-360=0

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Solution for x^2+17x-360=0 equation:


Simplifying
x2 + 17x + -360 = 0

Reorder the terms:
-360 + 17x + x2 = 0

Solving
-360 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + 17x + 360 + x2 = 0 + 360

Reorder the terms:
-360 + 360 + 17x + x2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + 17x + x2 = 0 + 360
17x + x2 = 0 + 360

Combine like terms: 0 + 360 = 360
17x + x2 = 360

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 360 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 360 + 72.25

Combine like terms: 360 + 72.25 = 432.25
72.25 + 17x + x2 = 432.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 432.25

Calculate the square root of the right side: 20.790622886

Break this problem into two subproblems by setting 
(x + 8.5) equal to 20.790622886 and -20.790622886.

Subproblem 1

x + 8.5 = 20.790622886 Simplifying x + 8.5 = 20.790622886 Reorder the terms: 8.5 + x = 20.790622886 Solving 8.5 + x = 20.790622886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 20.790622886 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 20.790622886 + -8.5 x = 20.790622886 + -8.5 Combine like terms: 20.790622886 + -8.5 = 12.290622886 x = 12.290622886 Simplifying x = 12.290622886

Subproblem 2

x + 8.5 = -20.790622886 Simplifying x + 8.5 = -20.790622886 Reorder the terms: 8.5 + x = -20.790622886 Solving 8.5 + x = -20.790622886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -20.790622886 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -20.790622886 + -8.5 x = -20.790622886 + -8.5 Combine like terms: -20.790622886 + -8.5 = -29.290622886 x = -29.290622886 Simplifying x = -29.290622886

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.290622886, -29.290622886}

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