x^2-5x-160=0

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Solution for x^2-5x-160=0 equation: 


Simplifying
x2 + -5x + -160 = 0

Reorder the terms:
-160 + -5x + x2 = 0

Solving
-160 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + -5x + 160 + x2 = 0 + 160

Reorder the terms:
-160 + 160 + -5x + x2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + -5x + x2 = 0 + 160
-5x + x2 = 0 + 160

Combine like terms: 0 + 160 = 160
-5x + x2 = 160

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 160 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 160 + 6.25

Combine like terms: 160 + 6.25 = 166.25
6.25 + -5x + x2 = 166.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 166.25

Calculate the square root of the right side: 12.893796958

Break this problem into two subproblems by setting 
(x + -2.5) equal to 12.893796958 and -12.893796958.


Subproblem 1
x + -2.5 = 12.893796958

Simplifying
x + -2.5 = 12.893796958

Reorder the terms:
-2.5 + x = 12.893796958

Solving
-2.5 + x = 12.893796958

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 12.893796958 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 12.893796958 + 2.5
x = 12.893796958 + 2.5

Combine like terms: 12.893796958 + 2.5 = 15.393796958
x = 15.393796958

Simplifying
x = 15.393796958


Subproblem 2
x + -2.5 = -12.893796958

Simplifying
x + -2.5 = -12.893796958

Reorder the terms:
-2.5 + x = -12.893796958

Solving
-2.5 + x = -12.893796958

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -12.893796958 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -12.893796958 + 2.5
x = -12.893796958 + 2.5

Combine like terms: -12.893796958 + 2.5 = -10.393796958
x = -10.393796958

Simplifying
x = -10.393796958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.393796958, -10.393796958}

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