x^2-16x-391=0

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Solution for x^2-16x-391=0 equation:


Simplifying
x2 + -16x + -391 = 0

Reorder the terms:
-391 + -16x + x2 = 0

Solving
-391 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '391' to each side of the equation.
-391 + -16x + 391 + x2 = 0 + 391

Reorder the terms:
-391 + 391 + -16x + x2 = 0 + 391

Combine like terms: -391 + 391 = 0
0 + -16x + x2 = 0 + 391
-16x + x2 = 0 + 391

Combine like terms: 0 + 391 = 391
-16x + x2 = 391

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 391 + 64

Reorder the terms:
64 + -16x + x2 = 391 + 64

Combine like terms: 391 + 64 = 455
64 + -16x + x2 = 455

Factor a perfect square on the left side:
(x + -8)(x + -8) = 455

Calculate the square root of the right side: 21.330729008

Break this problem into two subproblems by setting 
(x + -8) equal to 21.330729008 and -21.330729008.

Subproblem 1

x + -8 = 21.330729008 Simplifying x + -8 = 21.330729008 Reorder the terms: -8 + x = 21.330729008 Solving -8 + x = 21.330729008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 21.330729008 + 8 Combine like terms: -8 + 8 = 0 0 + x = 21.330729008 + 8 x = 21.330729008 + 8 Combine like terms: 21.330729008 + 8 = 29.330729008 x = 29.330729008 Simplifying x = 29.330729008

Subproblem 2

x + -8 = -21.330729008 Simplifying x + -8 = -21.330729008 Reorder the terms: -8 + x = -21.330729008 Solving -8 + x = -21.330729008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -21.330729008 + 8 Combine like terms: -8 + 8 = 0 0 + x = -21.330729008 + 8 x = -21.330729008 + 8 Combine like terms: -21.330729008 + 8 = -13.330729008 x = -13.330729008 Simplifying x = -13.330729008

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.330729008, -13.330729008}

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