14-2a(a+7)=

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Solution for 14-2a(a+7)= equation: 


Simplifying
14 + -2a(a + 7) = 0

Reorder the terms:
14 + -2a(7 + a) = 0
14 + (7 * -2a + a * -2a) = 0
14 + (-14a + -2a2) = 0

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

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -7a + -1a2) = 0

Ignore the factor 2.

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

Simplifying
7 + -7a + -1a2 = 0

Solving
7 + -7a + -1a2 = 0

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

Divide each side by '-1'.
-7 + 7a + a2 = 0

Move the constant term to the right:

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

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

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

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

The a term is 7a.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a + 12.25 + a2 = 7 + 12.25

Reorder the terms:
12.25 + 7a + a2 = 7 + 12.25

Combine like terms: 7 + 12.25 = 19.25
12.25 + 7a + a2 = 19.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(a + 3.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
a + 3.5 = 4.387482194

Simplifying
a + 3.5 = 4.387482194

Reorder the terms:
3.5 + a = 4.387482194

Solving
3.5 + a = 4.387482194

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = 4.387482194 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = 4.387482194 + -3.5
a = 4.387482194 + -3.5

Combine like terms: 4.387482194 + -3.5 = 0.887482194
a = 0.887482194

Simplifying
a = 0.887482194


Subproblem 2
a + 3.5 = -4.387482194

Simplifying
a + 3.5 = -4.387482194

Reorder the terms:
3.5 + a = -4.387482194

Solving
3.5 + a = -4.387482194

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = -4.387482194 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = -4.387482194 + -3.5
a = -4.387482194 + -3.5

Combine like terms: -4.387482194 + -3.5 = -7.887482194
a = -7.887482194

Simplifying
a = -7.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.887482194, -7.887482194}
Solution
a = {0.887482194, -7.887482194}

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