z^2-15z-156=0

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Solution for z^2-15z-156=0 equation:


Simplifying
z2 + -15z + -156 = 0

Reorder the terms:
-156 + -15z + z2 = 0

Solving
-156 + -15z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '156' to each side of the equation.
-156 + -15z + 156 + z2 = 0 + 156

Reorder the terms:
-156 + 156 + -15z + z2 = 0 + 156

Combine like terms: -156 + 156 = 0
0 + -15z + z2 = 0 + 156
-15z + z2 = 0 + 156

Combine like terms: 0 + 156 = 156
-15z + z2 = 156

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 = 156 + 56.25

Reorder the terms:
56.25 + -15z + z2 = 156 + 56.25

Combine like terms: 156 + 56.25 = 212.25
56.25 + -15z + z2 = 212.25

Factor a perfect square on the left side:
(z + -7.5)(z + -7.5) = 212.25

Calculate the square root of the right side: 14.568802284

Break this problem into two subproblems by setting 
(z + -7.5) equal to 14.568802284 and -14.568802284.

Subproblem 1

z + -7.5 = 14.568802284 Simplifying z + -7.5 = 14.568802284 Reorder the terms: -7.5 + z = 14.568802284 Solving -7.5 + z = 14.568802284 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 = 14.568802284 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = 14.568802284 + 7.5 z = 14.568802284 + 7.5 Combine like terms: 14.568802284 + 7.5 = 22.068802284 z = 22.068802284 Simplifying z = 22.068802284

Subproblem 2

z + -7.5 = -14.568802284 Simplifying z + -7.5 = -14.568802284 Reorder the terms: -7.5 + z = -14.568802284 Solving -7.5 + z = -14.568802284 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 = -14.568802284 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = -14.568802284 + 7.5 z = -14.568802284 + 7.5 Combine like terms: -14.568802284 + 7.5 = -7.068802284 z = -7.068802284 Simplifying z = -7.068802284

Solution

The solution to the problem is based on the solutions from the subproblems. z = {22.068802284, -7.068802284}

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