a^2+24a-200=0

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Solution for a^2+24a-200=0 equation:


Simplifying
a2 + 24a + -200 = 0

Reorder the terms:
-200 + 24a + a2 = 0

Solving
-200 + 24a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 24a + 200 + a2 = 0 + 200

Reorder the terms:
-200 + 200 + 24a + a2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 24a + a2 = 0 + 200
24a + a2 = 0 + 200

Combine like terms: 0 + 200 = 200
24a + a2 = 200

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 = 200 + 144

Reorder the terms:
144 + 24a + a2 = 200 + 144

Combine like terms: 200 + 144 = 344
144 + 24a + a2 = 344

Factor a perfect square on the left side:
(a + 12)(a + 12) = 344

Calculate the square root of the right side: 18.547236991

Break this problem into two subproblems by setting 
(a + 12) equal to 18.547236991 and -18.547236991.

Subproblem 1

a + 12 = 18.547236991 Simplifying a + 12 = 18.547236991 Reorder the terms: 12 + a = 18.547236991 Solving 12 + a = 18.547236991 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 = 18.547236991 + -12 Combine like terms: 12 + -12 = 0 0 + a = 18.547236991 + -12 a = 18.547236991 + -12 Combine like terms: 18.547236991 + -12 = 6.547236991 a = 6.547236991 Simplifying a = 6.547236991

Subproblem 2

a + 12 = -18.547236991 Simplifying a + 12 = -18.547236991 Reorder the terms: 12 + a = -18.547236991 Solving 12 + a = -18.547236991 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 = -18.547236991 + -12 Combine like terms: 12 + -12 = 0 0 + a = -18.547236991 + -12 a = -18.547236991 + -12 Combine like terms: -18.547236991 + -12 = -30.547236991 a = -30.547236991 Simplifying a = -30.547236991

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.547236991, -30.547236991}

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