x^2+9x-98=0

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Solution for x^2+9x-98=0 equation: 


Simplifying
x2 + 9x + -98 = 0

Reorder the terms:
-98 + 9x + x2 = 0

Solving
-98 + 9x + 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 + 9x + 98 + x2 = 0 + 98

Reorder the terms:
-98 + 98 + 9x + x2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + 9x + x2 = 0 + 98
9x + x2 = 0 + 98

Combine like terms: 0 + 98 = 98
9x + x2 = 98

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 98 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 98 + 20.25

Combine like terms: 98 + 20.25 = 118.25
20.25 + 9x + x2 = 118.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 118.25

Calculate the square root of the right side: 10.874281585

Break this problem into two subproblems by setting 
(x + 4.5) equal to 10.874281585 and -10.874281585.


Subproblem 1
x + 4.5 = 10.874281585

Simplifying
x + 4.5 = 10.874281585

Reorder the terms:
4.5 + x = 10.874281585

Solving
4.5 + x = 10.874281585

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 10.874281585 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 10.874281585 + -4.5
x = 10.874281585 + -4.5

Combine like terms: 10.874281585 + -4.5 = 6.374281585
x = 6.374281585

Simplifying
x = 6.374281585


Subproblem 2
x + 4.5 = -10.874281585

Simplifying
x + 4.5 = -10.874281585

Reorder the terms:
4.5 + x = -10.874281585

Solving
4.5 + x = -10.874281585

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -10.874281585 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -10.874281585 + -4.5
x = -10.874281585 + -4.5

Combine like terms: -10.874281585 + -4.5 = -15.374281585
x = -15.374281585

Simplifying
x = -15.374281585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.374281585, -15.374281585}

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