z^2+16z+49=0

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


Simplifying
z2 + 16z + 49 = 0

Reorder the terms:
49 + 16z + z2 = 0

Solving
49 + 16z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 16z + -49 + z2 = 0 + -49

Reorder the terms:
49 + -49 + 16z + z2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 16z + z2 = 0 + -49
16z + z2 = 0 + -49

Combine like terms: 0 + -49 = -49
16z + z2 = -49

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

Add '64' to each side of the equation.
16z + 64 + z2 = -49 + 64

Reorder the terms:
64 + 16z + z2 = -49 + 64

Combine like terms: -49 + 64 = 15
64 + 16z + z2 = 15

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

Calculate the square root of the right side: 3.872983346

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

Subproblem 1

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

Subproblem 2

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

Solution

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

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