z^2=15z+36

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Solution for z^2=15z+36 equation:


Simplifying
z2 = 15z + 36

Reorder the terms:
z2 = 36 + 15z

Solving
z2 = 36 + 15z

Solving for variable 'z'.

Reorder the terms:
-36 + -15z + z2 = 36 + 15z + -36 + -15z

Reorder the terms:
-36 + -15z + z2 = 36 + -36 + 15z + -15z

Combine like terms: 36 + -36 = 0
-36 + -15z + z2 = 0 + 15z + -15z
-36 + -15z + z2 = 15z + -15z

Combine like terms: 15z + -15z = 0
-36 + -15z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -15z + 36 + z2 = 0 + 36

Reorder the terms:
-36 + 36 + -15z + z2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -15z + z2 = 0 + 36
-15z + z2 = 0 + 36

Combine like terms: 0 + 36 = 36
-15z + z2 = 36

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 = 36 + 56.25

Reorder the terms:
56.25 + -15z + z2 = 36 + 56.25

Combine like terms: 36 + 56.25 = 92.25
56.25 + -15z + z2 = 92.25

Factor a perfect square on the left side:
(z + -7.5)(z + -7.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(z + -7.5) equal to 9.604686356 and -9.604686356.

Subproblem 1

z + -7.5 = 9.604686356 Simplifying z + -7.5 = 9.604686356 Reorder the terms: -7.5 + z = 9.604686356 Solving -7.5 + z = 9.604686356 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 = 9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = 9.604686356 + 7.5 z = 9.604686356 + 7.5 Combine like terms: 9.604686356 + 7.5 = 17.104686356 z = 17.104686356 Simplifying z = 17.104686356

Subproblem 2

z + -7.5 = -9.604686356 Simplifying z + -7.5 = -9.604686356 Reorder the terms: -7.5 + z = -9.604686356 Solving -7.5 + z = -9.604686356 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 = -9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = -9.604686356 + 7.5 z = -9.604686356 + 7.5 Combine like terms: -9.604686356 + 7.5 = -2.104686356 z = -2.104686356 Simplifying z = -2.104686356

Solution

The solution to the problem is based on the solutions from the subproblems. z = {17.104686356, -2.104686356}

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