a^2=24(a-1)

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Solution for a^2=24(a-1) equation:


Simplifying
a2 = 24(a + -1)

Reorder the terms:
a2 = 24(-1 + a)
a2 = (-1 * 24 + a * 24)
a2 = (-24 + 24a)

Solving
a2 = -24 + 24a

Solving for variable 'a'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -24 + 144

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

Combine like terms: -24 + 144 = 120
144 + -24a + a2 = 120

Factor a perfect square on the left side:
(a + -12)(a + -12) = 120

Calculate the square root of the right side: 10.95445115

Break this problem into two subproblems by setting 
(a + -12) equal to 10.95445115 and -10.95445115.

Subproblem 1

a + -12 = 10.95445115 Simplifying a + -12 = 10.95445115 Reorder the terms: -12 + a = 10.95445115 Solving -12 + a = 10.95445115 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 = 10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + a = 10.95445115 + 12 a = 10.95445115 + 12 Combine like terms: 10.95445115 + 12 = 22.95445115 a = 22.95445115 Simplifying a = 22.95445115

Subproblem 2

a + -12 = -10.95445115 Simplifying a + -12 = -10.95445115 Reorder the terms: -12 + a = -10.95445115 Solving -12 + a = -10.95445115 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 = -10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + a = -10.95445115 + 12 a = -10.95445115 + 12 Combine like terms: -10.95445115 + 12 = 1.04554885 a = 1.04554885 Simplifying a = 1.04554885

Solution

The solution to the problem is based on the solutions from the subproblems. a = {22.95445115, 1.04554885}

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