-2x^2+8x+160=0

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Solution for -2x^2+8x+160=0 equation: 


Simplifying
-2x2 + 8x + 160 = 0

Reorder the terms:
160 + 8x + -2x2 = 0

Solving
160 + 8x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(80 + 4x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(80 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
80 + 4x + -1x2 = 0

Solving
80 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-80 + -4x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -4x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -4x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -4x + x2 = 0 + 80
-4x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-4x + x2 = 80

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 80 + 4

Reorder the terms:
4 + -4x + x2 = 80 + 4

Combine like terms: 80 + 4 = 84
4 + -4x + x2 = 84

Factor a perfect square on the left side:
(x + -2)(x + -2) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + -2) equal to 9.16515139 and -9.16515139.


Subproblem 1
x + -2 = 9.16515139

Simplifying
x + -2 = 9.16515139

Reorder the terms:
-2 + x = 9.16515139

Solving
-2 + x = 9.16515139

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 9.16515139 + 2

Combine like terms: -2 + 2 = 0
0 + x = 9.16515139 + 2
x = 9.16515139 + 2

Combine like terms: 9.16515139 + 2 = 11.16515139
x = 11.16515139

Simplifying
x = 11.16515139


Subproblem 2
x + -2 = -9.16515139

Simplifying
x + -2 = -9.16515139

Reorder the terms:
-2 + x = -9.16515139

Solving
-2 + x = -9.16515139

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -9.16515139 + 2

Combine like terms: -2 + 2 = 0
0 + x = -9.16515139 + 2
x = -9.16515139 + 2

Combine like terms: -9.16515139 + 2 = -7.16515139
x = -7.16515139

Simplifying
x = -7.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.16515139, -7.16515139}
Solution
x = {11.16515139, -7.16515139}

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