1+8z+z^2=0

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Solution for 1+8z+z^2=0 equation:


Simplifying
1 + 8z + z2 = 0

Solving
1 + 8z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 8z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 8z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8z + z2 = 0 + -1
8z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
8z + z2 = -1

The z term is 8z.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8z + 16 + z2 = -1 + 16

Reorder the terms:
16 + 8z + z2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + 8z + z2 = 15

Factor a perfect square on the left side:
(z + 4)(z + 4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(z + 4) equal to 3.872983346 and -3.872983346.

Subproblem 1

z + 4 = 3.872983346 Simplifying z + 4 = 3.872983346 Reorder the terms: 4 + z = 3.872983346 Solving 4 + z = 3.872983346 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + z = 3.872983346 + -4 z = 3.872983346 + -4 Combine like terms: 3.872983346 + -4 = -0.127016654 z = -0.127016654 Simplifying z = -0.127016654

Subproblem 2

z + 4 = -3.872983346 Simplifying z + 4 = -3.872983346 Reorder the terms: 4 + z = -3.872983346 Solving 4 + z = -3.872983346 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = -3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + z = -3.872983346 + -4 z = -3.872983346 + -4 Combine like terms: -3.872983346 + -4 = -7.872983346 z = -7.872983346 Simplifying z = -7.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.127016654, -7.872983346}

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