z^2+15z+8=0

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Solution for z^2+15z+8=0 equation:


Simplifying
z2 + 15z + 8 = 0

Reorder the terms:
8 + 15z + z2 = 0

Solving
8 + 15z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 15z + -8 + z2 = 0 + -8

Reorder the terms:
8 + -8 + 15z + z2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 15z + z2 = 0 + -8
15z + z2 = 0 + -8

Combine like terms: 0 + -8 = -8
15z + z2 = -8

The z term is 15z.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15z + 56.25 + z2 = -8 + 56.25

Reorder the terms:
56.25 + 15z + z2 = -8 + 56.25

Combine like terms: -8 + 56.25 = 48.25
56.25 + 15z + z2 = 48.25

Factor a perfect square on the left side:
(z + 7.5)(z + 7.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(z + 7.5) equal to 6.946221995 and -6.946221995.

Subproblem 1

z + 7.5 = 6.946221995 Simplifying z + 7.5 = 6.946221995 Reorder the terms: 7.5 + z = 6.946221995 Solving 7.5 + z = 6.946221995 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + z = 6.946221995 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + z = 6.946221995 + -7.5 z = 6.946221995 + -7.5 Combine like terms: 6.946221995 + -7.5 = -0.553778005 z = -0.553778005 Simplifying z = -0.553778005

Subproblem 2

z + 7.5 = -6.946221995 Simplifying z + 7.5 = -6.946221995 Reorder the terms: 7.5 + z = -6.946221995 Solving 7.5 + z = -6.946221995 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + z = -6.946221995 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + z = -6.946221995 + -7.5 z = -6.946221995 + -7.5 Combine like terms: -6.946221995 + -7.5 = -14.446221995 z = -14.446221995 Simplifying z = -14.446221995

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.553778005, -14.446221995}

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