a^2-24a+120=0

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Solution for a^2-24a+120=0 equation:


Simplifying
a2 + -24a + 120 = 0

Reorder the terms:
120 + -24a + a2 = 0

Solving
120 + -24a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -24a + -120 + a2 = 0 + -120

Reorder the terms:
120 + -120 + -24a + a2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -24a + a2 = 0 + -120
-24a + a2 = 0 + -120

Combine like terms: 0 + -120 = -120
-24a + a2 = -120

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 = -120 + 144

Reorder the terms:
144 + -24a + a2 = -120 + 144

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

Factor a perfect square on the left side:
(a + -12)(a + -12) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(a + -12) equal to 4.898979486 and -4.898979486.

Subproblem 1

a + -12 = 4.898979486 Simplifying a + -12 = 4.898979486 Reorder the terms: -12 + a = 4.898979486 Solving -12 + a = 4.898979486 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 = 4.898979486 + 12 Combine like terms: -12 + 12 = 0 0 + a = 4.898979486 + 12 a = 4.898979486 + 12 Combine like terms: 4.898979486 + 12 = 16.898979486 a = 16.898979486 Simplifying a = 16.898979486

Subproblem 2

a + -12 = -4.898979486 Simplifying a + -12 = -4.898979486 Reorder the terms: -12 + a = -4.898979486 Solving -12 + a = -4.898979486 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 = -4.898979486 + 12 Combine like terms: -12 + 12 = 0 0 + a = -4.898979486 + 12 a = -4.898979486 + 12 Combine like terms: -4.898979486 + 12 = 7.101020514 a = 7.101020514 Simplifying a = 7.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. a = {16.898979486, 7.101020514}

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