a^2+12a+14=33

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Solution for a^2+12a+14=33 equation:


Simplifying
a2 + 12a + 14 = 33

Reorder the terms:
14 + 12a + a2 = 33

Solving
14 + 12a + a2 = 33

Solving for variable 'a'.

Reorder the terms:
14 + -33 + 12a + a2 = 33 + -33

Combine like terms: 14 + -33 = -19
-19 + 12a + a2 = 33 + -33

Combine like terms: 33 + -33 = 0
-19 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 12a + 19 + a2 = 0 + 19

Reorder the terms:
-19 + 19 + 12a + a2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 12a + a2 = 0 + 19
12a + a2 = 0 + 19

Combine like terms: 0 + 19 = 19
12a + a2 = 19

The a term is 12a.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12a + 36 + a2 = 19 + 36

Reorder the terms:
36 + 12a + a2 = 19 + 36

Combine like terms: 19 + 36 = 55
36 + 12a + a2 = 55

Factor a perfect square on the left side:
(a + 6)(a + 6) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(a + 6) equal to 7.416198487 and -7.416198487.

Subproblem 1

a + 6 = 7.416198487 Simplifying a + 6 = 7.416198487 Reorder the terms: 6 + a = 7.416198487 Solving 6 + a = 7.416198487 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + a = 7.416198487 + -6 a = 7.416198487 + -6 Combine like terms: 7.416198487 + -6 = 1.416198487 a = 1.416198487 Simplifying a = 1.416198487

Subproblem 2

a + 6 = -7.416198487 Simplifying a + 6 = -7.416198487 Reorder the terms: 6 + a = -7.416198487 Solving 6 + a = -7.416198487 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + a = -7.416198487 + -6 a = -7.416198487 + -6 Combine like terms: -7.416198487 + -6 = -13.416198487 a = -13.416198487 Simplifying a = -13.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.416198487, -13.416198487}

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