a^2-10a=21

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Solution for a^2-10a=21 equation:


Simplifying
a2 + -10a = 21

Reorder the terms:
-10a + a2 = 21

Solving
-10a + a2 = 21

Solving for variable 'a'.

Reorder the terms:
-21 + -10a + a2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -10a + 21 + a2 = 0 + 21

Reorder the terms:
-21 + 21 + -10a + a2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -10a + a2 = 0 + 21
-10a + a2 = 0 + 21

Combine like terms: 0 + 21 = 21
-10a + a2 = 21

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 = 21 + 25

Reorder the terms:
25 + -10a + a2 = 21 + 25

Combine like terms: 21 + 25 = 46
25 + -10a + a2 = 46

Factor a perfect square on the left side:
(a + -5)(a + -5) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(a + -5) equal to 6.782329983 and -6.782329983.

Subproblem 1

a + -5 = 6.782329983 Simplifying a + -5 = 6.782329983 Reorder the terms: -5 + a = 6.782329983 Solving -5 + a = 6.782329983 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 = 6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + a = 6.782329983 + 5 a = 6.782329983 + 5 Combine like terms: 6.782329983 + 5 = 11.782329983 a = 11.782329983 Simplifying a = 11.782329983

Subproblem 2

a + -5 = -6.782329983 Simplifying a + -5 = -6.782329983 Reorder the terms: -5 + a = -6.782329983 Solving -5 + a = -6.782329983 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 = -6.782329983 + 5 Combine like terms: -5 + 5 = 0 0 + a = -6.782329983 + 5 a = -6.782329983 + 5 Combine like terms: -6.782329983 + 5 = -1.782329983 a = -1.782329983 Simplifying a = -1.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. a = {11.782329983, -1.782329983}

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