a^2-2a=100

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Solution for a^2-2a=100 equation:


Simplifying
a2 + -2a = 100

Reorder the terms:
-2a + a2 = 100

Solving
-2a + a2 = 100

Solving for variable 'a'.

Reorder the terms:
-100 + -2a + a2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -2a + 100 + a2 = 0 + 100

Reorder the terms:
-100 + 100 + -2a + a2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -2a + a2 = 0 + 100
-2a + a2 = 0 + 100

Combine like terms: 0 + 100 = 100
-2a + a2 = 100

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

Add '1' to each side of the equation.
-2a + 1 + a2 = 100 + 1

Reorder the terms:
1 + -2a + a2 = 100 + 1

Combine like terms: 100 + 1 = 101
1 + -2a + a2 = 101

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

Calculate the square root of the right side: 10.049875621

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

Subproblem 1

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

Subproblem 2

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

Solution

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

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