x^2-8x-8498=0

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Solution for x^2-8x-8498=0 equation:


Simplifying
x2 + -8x + -8498 = 0

Reorder the terms:
-8498 + -8x + x2 = 0

Solving
-8498 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8498' to each side of the equation.
-8498 + -8x + 8498 + x2 = 0 + 8498

Reorder the terms:
-8498 + 8498 + -8x + x2 = 0 + 8498

Combine like terms: -8498 + 8498 = 0
0 + -8x + x2 = 0 + 8498
-8x + x2 = 0 + 8498

Combine like terms: 0 + 8498 = 8498
-8x + x2 = 8498

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 = 8498 + 16

Reorder the terms:
16 + -8x + x2 = 8498 + 16

Combine like terms: 8498 + 16 = 8514
16 + -8x + x2 = 8514

Factor a perfect square on the left side:
(x + -4)(x + -4) = 8514

Calculate the square root of the right side: 92.271338995

Break this problem into two subproblems by setting 
(x + -4) equal to 92.271338995 and -92.271338995.

Subproblem 1

x + -4 = 92.271338995 Simplifying x + -4 = 92.271338995 Reorder the terms: -4 + x = 92.271338995 Solving -4 + x = 92.271338995 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 = 92.271338995 + 4 Combine like terms: -4 + 4 = 0 0 + x = 92.271338995 + 4 x = 92.271338995 + 4 Combine like terms: 92.271338995 + 4 = 96.271338995 x = 96.271338995 Simplifying x = 96.271338995

Subproblem 2

x + -4 = -92.271338995 Simplifying x + -4 = -92.271338995 Reorder the terms: -4 + x = -92.271338995 Solving -4 + x = -92.271338995 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 = -92.271338995 + 4 Combine like terms: -4 + 4 = 0 0 + x = -92.271338995 + 4 x = -92.271338995 + 4 Combine like terms: -92.271338995 + 4 = -88.271338995 x = -88.271338995 Simplifying x = -88.271338995

Solution

The solution to the problem is based on the solutions from the subproblems. x = {96.271338995, -88.271338995}

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