x^2-4x-98=0

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Solution for x^2-4x-98=0 equation: 


Simplifying
x2 + -4x + -98 = 0

Reorder the terms:
-98 + -4x + x2 = 0

Solving
-98 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + -4x + 98 + x2 = 0 + 98

Reorder the terms:
-98 + 98 + -4x + x2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + -4x + x2 = 0 + 98
-4x + x2 = 0 + 98

Combine like terms: 0 + 98 = 98
-4x + x2 = 98

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 98 + 4

Reorder the terms:
4 + -4x + x2 = 98 + 4

Combine like terms: 98 + 4 = 102
4 + -4x + x2 = 102

Factor a perfect square on the left side:
(x + -2)(x + -2) = 102

Calculate the square root of the right side: 10.099504938

Break this problem into two subproblems by setting 
(x + -2) equal to 10.099504938 and -10.099504938.


Subproblem 1
x + -2 = 10.099504938

Simplifying
x + -2 = 10.099504938

Reorder the terms:
-2 + x = 10.099504938

Solving
-2 + x = 10.099504938

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 10.099504938 + 2

Combine like terms: -2 + 2 = 0
0 + x = 10.099504938 + 2
x = 10.099504938 + 2

Combine like terms: 10.099504938 + 2 = 12.099504938
x = 12.099504938

Simplifying
x = 12.099504938


Subproblem 2
x + -2 = -10.099504938

Simplifying
x + -2 = -10.099504938

Reorder the terms:
-2 + x = -10.099504938

Solving
-2 + x = -10.099504938

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -10.099504938 + 2

Combine like terms: -2 + 2 = 0
0 + x = -10.099504938 + 2
x = -10.099504938 + 2

Combine like terms: -10.099504938 + 2 = -8.099504938
x = -8.099504938

Simplifying
x = -8.099504938


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.099504938, -8.099504938}

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