x^2-8x-54=0

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Solution for x^2-8x-54=0 equation:


Simplifying
x2 + -8x + -54 = 0

Reorder the terms:
-54 + -8x + x2 = 0

Solving
-54 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -8x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -8x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -8x + x2 = 0 + 54
-8x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-8x + x2 = 54

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 54 + 16

Reorder the terms:
16 + -8x + x2 = 54 + 16

Combine like terms: 54 + 16 = 70
16 + -8x + x2 = 70

Factor a perfect square on the left side:
(x + -4)(x + -4) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + -4) equal to 8.366600265 and -8.366600265.

Subproblem 1

x + -4 = 8.366600265 Simplifying x + -4 = 8.366600265 Reorder the terms: -4 + x = 8.366600265 Solving -4 + x = 8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.366600265 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.366600265 + 4 x = 8.366600265 + 4 Combine like terms: 8.366600265 + 4 = 12.366600265 x = 12.366600265 Simplifying x = 12.366600265

Subproblem 2

x + -4 = -8.366600265 Simplifying x + -4 = -8.366600265 Reorder the terms: -4 + x = -8.366600265 Solving -4 + x = -8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.366600265 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.366600265 + 4 x = -8.366600265 + 4 Combine like terms: -8.366600265 + 4 = -4.366600265 x = -4.366600265 Simplifying x = -4.366600265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.366600265, -4.366600265}

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