x^2-2x-100=0

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


Simplifying
x2 + -2x + -100 = 0

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

Solving
-100 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -2x + 100 + x2 = 0 + 100

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

Combine like terms: -100 + 100 = 0
0 + -2x + x2 = 0 + 100
-2x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-2x + x2 = 100

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 100 + 1

Reorder the terms:
1 + -2x + x2 = 100 + 1

Combine like terms: 100 + 1 = 101
1 + -2x + x2 = 101

Factor a perfect square on the left side:
(x + -1)(x + -1) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x + -1) equal to 10.049875621 and -10.049875621.

Subproblem 1

x + -1 = 10.049875621 Simplifying x + -1 = 10.049875621 Reorder the terms: -1 + x = 10.049875621 Solving -1 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.049875621 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.049875621 + 1 x = 10.049875621 + 1 Combine like terms: 10.049875621 + 1 = 11.049875621 x = 11.049875621 Simplifying x = 11.049875621

Subproblem 2

x + -1 = -10.049875621 Simplifying x + -1 = -10.049875621 Reorder the terms: -1 + x = -10.049875621 Solving -1 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.049875621 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.049875621 + 1 x = -10.049875621 + 1 Combine like terms: -10.049875621 + 1 = -9.049875621 x = -9.049875621 Simplifying x = -9.049875621

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.049875621, -9.049875621}

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