-a^2-28a+192=0

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Solution for -a^2-28a+192=0 equation:


Simplifying
-1a2 + -28a + 192 = 0

Reorder the terms:
192 + -28a + -1a2 = 0

Solving
192 + -28a + -1a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-192 + 28a + a2 = 0

Move the constant term to the right:

Add '192' to each side of the equation.
-192 + 28a + 192 + a2 = 0 + 192

Reorder the terms:
-192 + 192 + 28a + a2 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + 28a + a2 = 0 + 192
28a + a2 = 0 + 192

Combine like terms: 0 + 192 = 192
28a + a2 = 192

The a term is 28a.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28a + 196 + a2 = 192 + 196

Reorder the terms:
196 + 28a + a2 = 192 + 196

Combine like terms: 192 + 196 = 388
196 + 28a + a2 = 388

Factor a perfect square on the left side:
(a + 14)(a + 14) = 388

Calculate the square root of the right side: 19.697715604

Break this problem into two subproblems by setting 
(a + 14) equal to 19.697715604 and -19.697715604.

Subproblem 1

a + 14 = 19.697715604 Simplifying a + 14 = 19.697715604 Reorder the terms: 14 + a = 19.697715604 Solving 14 + a = 19.697715604 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + a = 19.697715604 + -14 Combine like terms: 14 + -14 = 0 0 + a = 19.697715604 + -14 a = 19.697715604 + -14 Combine like terms: 19.697715604 + -14 = 5.697715604 a = 5.697715604 Simplifying a = 5.697715604

Subproblem 2

a + 14 = -19.697715604 Simplifying a + 14 = -19.697715604 Reorder the terms: 14 + a = -19.697715604 Solving 14 + a = -19.697715604 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + a = -19.697715604 + -14 Combine like terms: 14 + -14 = 0 0 + a = -19.697715604 + -14 a = -19.697715604 + -14 Combine like terms: -19.697715604 + -14 = -33.697715604 a = -33.697715604 Simplifying a = -33.697715604

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.697715604, -33.697715604}

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