a^2+16a+49=0

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Solution for a^2+16a+49=0 equation:


Simplifying
a2 + 16a + 49 = 0

Reorder the terms:
49 + 16a + a2 = 0

Solving
49 + 16a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 16a + -49 + a2 = 0 + -49

Reorder the terms:
49 + -49 + 16a + a2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 16a + a2 = 0 + -49
16a + a2 = 0 + -49

Combine like terms: 0 + -49 = -49
16a + a2 = -49

The a term is 16a.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16a + 64 + a2 = -49 + 64

Reorder the terms:
64 + 16a + a2 = -49 + 64

Combine like terms: -49 + 64 = 15
64 + 16a + a2 = 15

Factor a perfect square on the left side:
(a + 8)(a + 8) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(a + 8) equal to 3.872983346 and -3.872983346.

Subproblem 1

a + 8 = 3.872983346 Simplifying a + 8 = 3.872983346 Reorder the terms: 8 + a = 3.872983346 Solving 8 + a = 3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = 3.872983346 + -8 Combine like terms: 8 + -8 = 0 0 + a = 3.872983346 + -8 a = 3.872983346 + -8 Combine like terms: 3.872983346 + -8 = -4.127016654 a = -4.127016654 Simplifying a = -4.127016654

Subproblem 2

a + 8 = -3.872983346 Simplifying a + 8 = -3.872983346 Reorder the terms: 8 + a = -3.872983346 Solving 8 + a = -3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a = -3.872983346 + -8 Combine like terms: 8 + -8 = 0 0 + a = -3.872983346 + -8 a = -3.872983346 + -8 Combine like terms: -3.872983346 + -8 = -11.872983346 a = -11.872983346 Simplifying a = -11.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-4.127016654, -11.872983346}

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