a^2-10a=100

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Solution for a^2-10a=100 equation:


Simplifying
a2 + -10a = 100

Reorder the terms:
-10a + a2 = 100

Solving
-10a + a2 = 100

Solving for variable 'a'.

Reorder the terms:
-100 + -10a + a2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + -10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -10a + 100 + a2 = 0 + 100

Reorder the terms:
-100 + 100 + -10a + a2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -10a + a2 = 0 + 100
-10a + a2 = 0 + 100

Combine like terms: 0 + 100 = 100
-10a + a2 = 100

The a term is -10a.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10a + 25 + a2 = 100 + 25

Reorder the terms:
25 + -10a + a2 = 100 + 25

Combine like terms: 100 + 25 = 125
25 + -10a + a2 = 125

Factor a perfect square on the left side:
(a + -5)(a + -5) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(a + -5) equal to 11.180339887 and -11.180339887.

Subproblem 1

a + -5 = 11.180339887 Simplifying a + -5 = 11.180339887 Reorder the terms: -5 + a = 11.180339887 Solving -5 + a = 11.180339887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + a = 11.180339887 + 5 a = 11.180339887 + 5 Combine like terms: 11.180339887 + 5 = 16.180339887 a = 16.180339887 Simplifying a = 16.180339887

Subproblem 2

a + -5 = -11.180339887 Simplifying a + -5 = -11.180339887 Reorder the terms: -5 + a = -11.180339887 Solving -5 + a = -11.180339887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -11.180339887 + 5 Combine like terms: -5 + 5 = 0 0 + a = -11.180339887 + 5 a = -11.180339887 + 5 Combine like terms: -11.180339887 + 5 = -6.180339887 a = -6.180339887 Simplifying a = -6.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. a = {16.180339887, -6.180339887}

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