2x^2-62x-162=0

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Solution for 2x^2-62x-162=0 equation: 


Simplifying
2x2 + -62x + -162 = 0

Reorder the terms:
-162 + -62x + 2x2 = 0

Solving
-162 + -62x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-81 + -31x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-81 + -31x + x2)' equal to zero and attempt to solve:

Simplifying
-81 + -31x + x2 = 0

Solving
-81 + -31x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -31x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -31x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -31x + x2 = 0 + 81
-31x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-31x + x2 = 81

The x term is -31x.  Take half its coefficient (-15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
-31x + 240.25 + x2 = 81 + 240.25

Reorder the terms:
240.25 + -31x + x2 = 81 + 240.25

Combine like terms: 81 + 240.25 = 321.25
240.25 + -31x + x2 = 321.25

Factor a perfect square on the left side:
(x + -15.5)(x + -15.5) = 321.25

Calculate the square root of the right side: 17.923448329

Break this problem into two subproblems by setting 
(x + -15.5) equal to 17.923448329 and -17.923448329.


Subproblem 1
x + -15.5 = 17.923448329

Simplifying
x + -15.5 = 17.923448329

Reorder the terms:
-15.5 + x = 17.923448329

Solving
-15.5 + x = 17.923448329

Solving for variable 'x'.

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

Add '15.5' to each side of the equation.
-15.5 + 15.5 + x = 17.923448329 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + x = 17.923448329 + 15.5
x = 17.923448329 + 15.5

Combine like terms: 17.923448329 + 15.5 = 33.423448329
x = 33.423448329

Simplifying
x = 33.423448329


Subproblem 2
x + -15.5 = -17.923448329

Simplifying
x + -15.5 = -17.923448329

Reorder the terms:
-15.5 + x = -17.923448329

Solving
-15.5 + x = -17.923448329

Solving for variable 'x'.

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

Add '15.5' to each side of the equation.
-15.5 + 15.5 + x = -17.923448329 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + x = -17.923448329 + 15.5
x = -17.923448329 + 15.5

Combine like terms: -17.923448329 + 15.5 = -2.423448329
x = -2.423448329

Simplifying
x = -2.423448329


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.423448329, -2.423448329}
Solution
x = {33.423448329, -2.423448329}

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