z^2+16z=-47

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Solution for z^2+16z=-47 equation:


Simplifying
z2 + 16z = -47

Reorder the terms:
16z + z2 = -47

Solving
16z + z2 = -47

Solving for variable 'z'.

Reorder the terms:
47 + 16z + z2 = -47 + 47

Combine like terms: -47 + 47 = 0
47 + 16z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 16z + -47 + z2 = 0 + -47

Reorder the terms:
47 + -47 + 16z + z2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 16z + z2 = 0 + -47
16z + z2 = 0 + -47

Combine like terms: 0 + -47 = -47
16z + z2 = -47

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 = -47 + 64

Reorder the terms:
64 + 16z + z2 = -47 + 64

Combine like terms: -47 + 64 = 17
64 + 16z + z2 = 17

Factor a perfect square on the left side:
(z + 8)(z + 8) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(z + 8) equal to 4.123105626 and -4.123105626.

Subproblem 1

z + 8 = 4.123105626 Simplifying z + 8 = 4.123105626 Reorder the terms: 8 + z = 4.123105626 Solving 8 + z = 4.123105626 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 = 4.123105626 + -8 Combine like terms: 8 + -8 = 0 0 + z = 4.123105626 + -8 z = 4.123105626 + -8 Combine like terms: 4.123105626 + -8 = -3.876894374 z = -3.876894374 Simplifying z = -3.876894374

Subproblem 2

z + 8 = -4.123105626 Simplifying z + 8 = -4.123105626 Reorder the terms: 8 + z = -4.123105626 Solving 8 + z = -4.123105626 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 = -4.123105626 + -8 Combine like terms: 8 + -8 = 0 0 + z = -4.123105626 + -8 z = -4.123105626 + -8 Combine like terms: -4.123105626 + -8 = -12.123105626 z = -12.123105626 Simplifying z = -12.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-3.876894374, -12.123105626}

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