x^2-16x=6

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Solution for x^2-16x=6 equation:


Simplifying
x2 + -16x = 6

Reorder the terms:
-16x + x2 = 6

Solving
-16x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + -16x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -16x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -16x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -16x + x2 = 0 + 6
-16x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-16x + x2 = 6

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 = 6 + 64

Reorder the terms:
64 + -16x + x2 = 6 + 64

Combine like terms: 6 + 64 = 70
64 + -16x + x2 = 70

Factor a perfect square on the left side:
(x + -8)(x + -8) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + -8) equal to 8.366600265 and -8.366600265.

Subproblem 1

x + -8 = 8.366600265 Simplifying x + -8 = 8.366600265 Reorder the terms: -8 + x = 8.366600265 Solving -8 + x = 8.366600265 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 = 8.366600265 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.366600265 + 8 x = 8.366600265 + 8 Combine like terms: 8.366600265 + 8 = 16.366600265 x = 16.366600265 Simplifying x = 16.366600265

Subproblem 2

x + -8 = -8.366600265 Simplifying x + -8 = -8.366600265 Reorder the terms: -8 + x = -8.366600265 Solving -8 + x = -8.366600265 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 = -8.366600265 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.366600265 + 8 x = -8.366600265 + 8 Combine like terms: -8.366600265 + 8 = -0.366600265 x = -0.366600265 Simplifying x = -0.366600265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.366600265, -0.366600265}

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