a^2-28a+192=20

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Solution for a^2-28a+192=20 equation:


Simplifying
a2 + -28a + 192 = 20

Reorder the terms:
192 + -28a + a2 = 20

Solving
192 + -28a + a2 = 20

Solving for variable 'a'.

Reorder the terms:
192 + -20 + -28a + a2 = 20 + -20

Combine like terms: 192 + -20 = 172
172 + -28a + a2 = 20 + -20

Combine like terms: 20 + -20 = 0
172 + -28a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-172' to each side of the equation.
172 + -28a + -172 + a2 = 0 + -172

Reorder the terms:
172 + -172 + -28a + a2 = 0 + -172

Combine like terms: 172 + -172 = 0
0 + -28a + a2 = 0 + -172
-28a + a2 = 0 + -172

Combine like terms: 0 + -172 = -172
-28a + a2 = -172

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 = -172 + 196

Reorder the terms:
196 + -28a + a2 = -172 + 196

Combine like terms: -172 + 196 = 24
196 + -28a + a2 = 24

Factor a perfect square on the left side:
(a + -14)(a + -14) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(a + -14) equal to 4.898979486 and -4.898979486.

Subproblem 1

a + -14 = 4.898979486 Simplifying a + -14 = 4.898979486 Reorder the terms: -14 + a = 4.898979486 Solving -14 + a = 4.898979486 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 = 4.898979486 + 14 Combine like terms: -14 + 14 = 0 0 + a = 4.898979486 + 14 a = 4.898979486 + 14 Combine like terms: 4.898979486 + 14 = 18.898979486 a = 18.898979486 Simplifying a = 18.898979486

Subproblem 2

a + -14 = -4.898979486 Simplifying a + -14 = -4.898979486 Reorder the terms: -14 + a = -4.898979486 Solving -14 + a = -4.898979486 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 = -4.898979486 + 14 Combine like terms: -14 + 14 = 0 0 + a = -4.898979486 + 14 a = -4.898979486 + 14 Combine like terms: -4.898979486 + 14 = 9.101020514 a = 9.101020514 Simplifying a = 9.101020514

Solution

The solution to the problem is based on the solutions from the subproblems. a = {18.898979486, 9.101020514}

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