a^2-10a=23

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Solution for a^2-10a=23 equation:


Simplifying
a2 + -10a = 23

Reorder the terms:
-10a + a2 = 23

Solving
-10a + a2 = 23

Solving for variable 'a'.

Reorder the terms:
-23 + -10a + a2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -10a + 23 + a2 = 0 + 23

Reorder the terms:
-23 + 23 + -10a + a2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -10a + a2 = 0 + 23
-10a + a2 = 0 + 23

Combine like terms: 0 + 23 = 23
-10a + a2 = 23

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 = 23 + 25

Reorder the terms:
25 + -10a + a2 = 23 + 25

Combine like terms: 23 + 25 = 48
25 + -10a + a2 = 48

Factor a perfect square on the left side:
(a + -5)(a + -5) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(a + -5) equal to 6.92820323 and -6.92820323.

Subproblem 1

a + -5 = 6.92820323 Simplifying a + -5 = 6.92820323 Reorder the terms: -5 + a = 6.92820323 Solving -5 + a = 6.92820323 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 = 6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + a = 6.92820323 + 5 a = 6.92820323 + 5 Combine like terms: 6.92820323 + 5 = 11.92820323 a = 11.92820323 Simplifying a = 11.92820323

Subproblem 2

a + -5 = -6.92820323 Simplifying a + -5 = -6.92820323 Reorder the terms: -5 + a = -6.92820323 Solving -5 + a = -6.92820323 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 = -6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + a = -6.92820323 + 5 a = -6.92820323 + 5 Combine like terms: -6.92820323 + 5 = -1.92820323 a = -1.92820323 Simplifying a = -1.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. a = {11.92820323, -1.92820323}

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