a^2+24a-48=0

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Solution for a^2+24a-48=0 equation:


Simplifying
a2 + 24a + -48 = 0

Reorder the terms:
-48 + 24a + a2 = 0

Solving
-48 + 24a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 24a + 48 + a2 = 0 + 48

Reorder the terms:
-48 + 48 + 24a + a2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 24a + a2 = 0 + 48
24a + a2 = 0 + 48

Combine like terms: 0 + 48 = 48
24a + a2 = 48

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 = 48 + 144

Reorder the terms:
144 + 24a + a2 = 48 + 144

Combine like terms: 48 + 144 = 192
144 + 24a + a2 = 192

Factor a perfect square on the left side:
(a + 12)(a + 12) = 192

Calculate the square root of the right side: 13.856406461

Break this problem into two subproblems by setting 
(a + 12) equal to 13.856406461 and -13.856406461.

Subproblem 1

a + 12 = 13.856406461 Simplifying a + 12 = 13.856406461 Reorder the terms: 12 + a = 13.856406461 Solving 12 + a = 13.856406461 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 = 13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + a = 13.856406461 + -12 a = 13.856406461 + -12 Combine like terms: 13.856406461 + -12 = 1.856406461 a = 1.856406461 Simplifying a = 1.856406461

Subproblem 2

a + 12 = -13.856406461 Simplifying a + 12 = -13.856406461 Reorder the terms: 12 + a = -13.856406461 Solving 12 + a = -13.856406461 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 = -13.856406461 + -12 Combine like terms: 12 + -12 = 0 0 + a = -13.856406461 + -12 a = -13.856406461 + -12 Combine like terms: -13.856406461 + -12 = -25.856406461 a = -25.856406461 Simplifying a = -25.856406461

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.856406461, -25.856406461}

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