100x^2-99x-2=0

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Solution for 100x^2-99x-2=0 equation:


Simplifying
100x2 + -99x + -2 = 0

Reorder the terms:
-2 + -99x + 100x2 = 0

Solving
-2 + -99x + 100x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
100 the coefficient of the squared term: 

Divide each side by '100'.
-0.02 + -0.99x + x2 = 0

Move the constant term to the right:

Add '0.02' to each side of the equation.
-0.02 + -0.99x + 0.02 + x2 = 0 + 0.02

Reorder the terms:
-0.02 + 0.02 + -0.99x + x2 = 0 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + -0.99x + x2 = 0 + 0.02
-0.99x + x2 = 0 + 0.02

Combine like terms: 0 + 0.02 = 0.02
-0.99x + x2 = 0.02

The x term is -0.99x.  Take half its coefficient (-0.495).
Square it (0.245025) and add it to both sides.

Add '0.245025' to each side of the equation.
-0.99x + 0.245025 + x2 = 0.02 + 0.245025

Reorder the terms:
0.245025 + -0.99x + x2 = 0.02 + 0.245025

Combine like terms: 0.02 + 0.245025 = 0.265025
0.245025 + -0.99x + x2 = 0.265025

Factor a perfect square on the left side:
(x + -0.495)(x + -0.495) = 0.265025

Calculate the square root of the right side: 0.514805789

Break this problem into two subproblems by setting 
(x + -0.495) equal to 0.514805789 and -0.514805789.

Subproblem 1

x + -0.495 = 0.514805789 Simplifying x + -0.495 = 0.514805789 Reorder the terms: -0.495 + x = 0.514805789 Solving -0.495 + x = 0.514805789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.495' to each side of the equation. -0.495 + 0.495 + x = 0.514805789 + 0.495 Combine like terms: -0.495 + 0.495 = 0.000 0.000 + x = 0.514805789 + 0.495 x = 0.514805789 + 0.495 Combine like terms: 0.514805789 + 0.495 = 1.009805789 x = 1.009805789 Simplifying x = 1.009805789

Subproblem 2

x + -0.495 = -0.514805789 Simplifying x + -0.495 = -0.514805789 Reorder the terms: -0.495 + x = -0.514805789 Solving -0.495 + x = -0.514805789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.495' to each side of the equation. -0.495 + 0.495 + x = -0.514805789 + 0.495 Combine like terms: -0.495 + 0.495 = 0.000 0.000 + x = -0.514805789 + 0.495 x = -0.514805789 + 0.495 Combine like terms: -0.514805789 + 0.495 = -0.019805789 x = -0.019805789 Simplifying x = -0.019805789

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.009805789, -0.019805789}

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