x^2+16x-1=0

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Solution for x^2+16x-1=0 equation:


Simplifying
x2 + 16x + -1 = 0

Reorder the terms:
-1 + 16x + x2 = 0

Solving
-1 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 16x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 16x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16x + x2 = 0 + 1
16x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
16x + x2 = 1

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 = 1 + 64

Reorder the terms:
64 + 16x + x2 = 1 + 64

Combine like terms: 1 + 64 = 65
64 + 16x + x2 = 65

Factor a perfect square on the left side:
(x + 8)(x + 8) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + 8) equal to 8.062257748 and -8.062257748.

Subproblem 1

x + 8 = 8.062257748 Simplifying x + 8 = 8.062257748 Reorder the terms: 8 + x = 8.062257748 Solving 8 + x = 8.062257748 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 = 8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.062257748 + -8 x = 8.062257748 + -8 Combine like terms: 8.062257748 + -8 = 0.062257748 x = 0.062257748 Simplifying x = 0.062257748

Subproblem 2

x + 8 = -8.062257748 Simplifying x + 8 = -8.062257748 Reorder the terms: 8 + x = -8.062257748 Solving 8 + x = -8.062257748 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 = -8.062257748 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.062257748 + -8 x = -8.062257748 + -8 Combine like terms: -8.062257748 + -8 = -16.062257748 x = -16.062257748 Simplifying x = -16.062257748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.062257748, -16.062257748}

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