a^2-24a=16

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Solution for a^2-24a=16 equation:


Simplifying
a2 + -24a = 16

Reorder the terms:
-24a + a2 = 16

Solving
-24a + a2 = 16

Solving for variable 'a'.

Reorder the terms:
-16 + -24a + a2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -24a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -24a + 16 + a2 = 0 + 16

Reorder the terms:
-16 + 16 + -24a + a2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -24a + a2 = 0 + 16
-24a + a2 = 0 + 16

Combine like terms: 0 + 16 = 16
-24a + a2 = 16

The a term is -24a.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24a + 144 + a2 = 16 + 144

Reorder the terms:
144 + -24a + a2 = 16 + 144

Combine like terms: 16 + 144 = 160
144 + -24a + a2 = 160

Factor a perfect square on the left side:
(a + -12)(a + -12) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(a + -12) equal to 12.649110641 and -12.649110641.

Subproblem 1

a + -12 = 12.649110641 Simplifying a + -12 = 12.649110641 Reorder the terms: -12 + a = 12.649110641 Solving -12 + a = 12.649110641 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = 12.649110641 + 12 Combine like terms: -12 + 12 = 0 0 + a = 12.649110641 + 12 a = 12.649110641 + 12 Combine like terms: 12.649110641 + 12 = 24.649110641 a = 24.649110641 Simplifying a = 24.649110641

Subproblem 2

a + -12 = -12.649110641 Simplifying a + -12 = -12.649110641 Reorder the terms: -12 + a = -12.649110641 Solving -12 + a = -12.649110641 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = -12.649110641 + 12 Combine like terms: -12 + 12 = 0 0 + a = -12.649110641 + 12 a = -12.649110641 + 12 Combine like terms: -12.649110641 + 12 = -0.649110641 a = -0.649110641 Simplifying a = -0.649110641

Solution

The solution to the problem is based on the solutions from the subproblems. a = {24.649110641, -0.649110641}

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