a^2+14a+12=8

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Solution for a^2+14a+12=8 equation:


Simplifying
a2 + 14a + 12 = 8

Reorder the terms:
12 + 14a + a2 = 8

Solving
12 + 14a + a2 = 8

Solving for variable 'a'.

Reorder the terms:
12 + -8 + 14a + a2 = 8 + -8

Combine like terms: 12 + -8 = 4
4 + 14a + a2 = 8 + -8

Combine like terms: 8 + -8 = 0
4 + 14a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 14a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + 14a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 14a + a2 = 0 + -4
14a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
14a + a2 = -4

The a term is 14a.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14a + 49 + a2 = -4 + 49

Reorder the terms:
49 + 14a + a2 = -4 + 49

Combine like terms: -4 + 49 = 45
49 + 14a + a2 = 45

Factor a perfect square on the left side:
(a + 7)(a + 7) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(a + 7) equal to 6.708203933 and -6.708203933.

Subproblem 1

a + 7 = 6.708203933 Simplifying a + 7 = 6.708203933 Reorder the terms: 7 + a = 6.708203933 Solving 7 + a = 6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + a = 6.708203933 + -7 a = 6.708203933 + -7 Combine like terms: 6.708203933 + -7 = -0.291796067 a = -0.291796067 Simplifying a = -0.291796067

Subproblem 2

a + 7 = -6.708203933 Simplifying a + 7 = -6.708203933 Reorder the terms: 7 + a = -6.708203933 Solving 7 + a = -6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = -6.708203933 + -7 Combine like terms: 7 + -7 = 0 0 + a = -6.708203933 + -7 a = -6.708203933 + -7 Combine like terms: -6.708203933 + -7 = -13.708203933 a = -13.708203933 Simplifying a = -13.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.291796067, -13.708203933}

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