7a-a^2+16=

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Solution for 7a-a^2+16= equation:


Simplifying
7a + -1a2 + 16 = 0

Reorder the terms:
16 + 7a + -1a2 = 0

Solving
16 + 7a + -1a2 = 0

Solving for variable 'a'.

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

Divide each side by '-1'.
-16 + -7a + a2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -7a + 16 + a2 = 0 + 16

Reorder the terms:
-16 + 16 + -7a + a2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -7a + a2 = 0 + 16
-7a + a2 = 0 + 16

Combine like terms: 0 + 16 = 16
-7a + a2 = 16

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 = 16 + 12.25

Reorder the terms:
12.25 + -7a + a2 = 16 + 12.25

Combine like terms: 16 + 12.25 = 28.25
12.25 + -7a + a2 = 28.25

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(a + -3.5) equal to 5.315072906 and -5.315072906.

Subproblem 1

a + -3.5 = 5.315072906 Simplifying a + -3.5 = 5.315072906 Reorder the terms: -3.5 + a = 5.315072906 Solving -3.5 + a = 5.315072906 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 = 5.315072906 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 5.315072906 + 3.5 a = 5.315072906 + 3.5 Combine like terms: 5.315072906 + 3.5 = 8.815072906 a = 8.815072906 Simplifying a = 8.815072906

Subproblem 2

a + -3.5 = -5.315072906 Simplifying a + -3.5 = -5.315072906 Reorder the terms: -3.5 + a = -5.315072906 Solving -3.5 + a = -5.315072906 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 = -5.315072906 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -5.315072906 + 3.5 a = -5.315072906 + 3.5 Combine like terms: -5.315072906 + 3.5 = -1.815072906 a = -1.815072906 Simplifying a = -1.815072906

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.815072906, -1.815072906}

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