2a^2-16a-14=0

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Solution for 2a^2-16a-14=0 equation: 


Simplifying
2a2 + -16a + -14 = 0

Reorder the terms:
-14 + -16a + 2a2 = 0

Solving
-14 + -16a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -8a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -8a + a2)' equal to zero and attempt to solve:

Simplifying
-7 + -8a + a2 = 0

Solving
-7 + -8a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -8a + 7 + a2 = 0 + 7

Reorder the terms:
-7 + 7 + -8a + a2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8a + a2 = 0 + 7
-8a + a2 = 0 + 7

Combine like terms: 0 + 7 = 7
-8a + a2 = 7

The a term is -8a.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8a + 16 + a2 = 7 + 16

Reorder the terms:
16 + -8a + a2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + -8a + a2 = 23

Factor a perfect square on the left side:
(a + -4)(a + -4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(a + -4) equal to 4.795831523 and -4.795831523.


Subproblem 1
a + -4 = 4.795831523

Simplifying
a + -4 = 4.795831523

Reorder the terms:
-4 + a = 4.795831523

Solving
-4 + a = 4.795831523

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + a = 4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + a = 4.795831523 + 4
a = 4.795831523 + 4

Combine like terms: 4.795831523 + 4 = 8.795831523
a = 8.795831523

Simplifying
a = 8.795831523


Subproblem 2
a + -4 = -4.795831523

Simplifying
a + -4 = -4.795831523

Reorder the terms:
-4 + a = -4.795831523

Solving
-4 + a = -4.795831523

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + a = -4.795831523 + 4

Combine like terms: -4 + 4 = 0
0 + a = -4.795831523 + 4
a = -4.795831523 + 4

Combine like terms: -4.795831523 + 4 = -0.795831523
a = -0.795831523

Simplifying
a = -0.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {8.795831523, -0.795831523}
Solution
a = {8.795831523, -0.795831523}

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