(x^2)-98.7x-1141.9=0

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Solution for (x^2)-98.7x-1141.9=0 equation: 


Simplifying
(x2) + -98.7x + -1141.9 = 0
x2 + -98.7x + -1141.9 = 0

Reorder the terms:
-1141.9 + -98.7x + x2 = 0

Solving
-1141.9 + -98.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1141.9' to each side of the equation.
-1141.9 + -98.7x + 1141.9 + x2 = 0 + 1141.9

Reorder the terms:
-1141.9 + 1141.9 + -98.7x + x2 = 0 + 1141.9

Combine like terms: -1141.9 + 1141.9 = 0.0
0.0 + -98.7x + x2 = 0 + 1141.9
-98.7x + x2 = 0 + 1141.9

Combine like terms: 0 + 1141.9 = 1141.9
-98.7x + x2 = 1141.9

The x term is -98.7x.  Take half its coefficient (-49.35).
Square it (2435.4225) and add it to both sides.

Add '2435.4225' to each side of the equation.
-98.7x + 2435.4225 + x2 = 1141.9 + 2435.4225

Reorder the terms:
2435.4225 + -98.7x + x2 = 1141.9 + 2435.4225

Combine like terms: 1141.9 + 2435.4225 = 3577.3225
2435.4225 + -98.7x + x2 = 3577.3225

Factor a perfect square on the left side:
(x + -49.35)(x + -49.35) = 3577.3225

Calculate the square root of the right side: 59.810722283

Break this problem into two subproblems by setting 
(x + -49.35) equal to 59.810722283 and -59.810722283.


Subproblem 1
x + -49.35 = 59.810722283

Simplifying
x + -49.35 = 59.810722283

Reorder the terms:
-49.35 + x = 59.810722283

Solving
-49.35 + x = 59.810722283

Solving for variable 'x'.

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

Add '49.35' to each side of the equation.
-49.35 + 49.35 + x = 59.810722283 + 49.35

Combine like terms: -49.35 + 49.35 = 0.00
0.00 + x = 59.810722283 + 49.35
x = 59.810722283 + 49.35

Combine like terms: 59.810722283 + 49.35 = 109.160722283
x = 109.160722283

Simplifying
x = 109.160722283


Subproblem 2
x + -49.35 = -59.810722283

Simplifying
x + -49.35 = -59.810722283

Reorder the terms:
-49.35 + x = -59.810722283

Solving
-49.35 + x = -59.810722283

Solving for variable 'x'.

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

Add '49.35' to each side of the equation.
-49.35 + 49.35 + x = -59.810722283 + 49.35

Combine like terms: -49.35 + 49.35 = 0.00
0.00 + x = -59.810722283 + 49.35
x = -59.810722283 + 49.35

Combine like terms: -59.810722283 + 49.35 = -10.460722283
x = -10.460722283

Simplifying
x = -10.460722283


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {109.160722283, -10.460722283}

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