z^2-12z=-15

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Solution for z^2-12z=-15 equation:


Simplifying
z2 + -12z = -15

Reorder the terms:
-12z + z2 = -15

Solving
-12z + z2 = -15

Solving for variable 'z'.

Reorder the terms:
15 + -12z + z2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -12z + -15 + z2 = 0 + -15

Reorder the terms:
15 + -15 + -12z + z2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -12z + z2 = 0 + -15
-12z + z2 = 0 + -15

Combine like terms: 0 + -15 = -15
-12z + z2 = -15

The z term is -12z.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12z + 36 + z2 = -15 + 36

Reorder the terms:
36 + -12z + z2 = -15 + 36

Combine like terms: -15 + 36 = 21
36 + -12z + z2 = 21

Factor a perfect square on the left side:
(z + -6)(z + -6) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(z + -6) equal to 4.582575695 and -4.582575695.

Subproblem 1

z + -6 = 4.582575695 Simplifying z + -6 = 4.582575695 Reorder the terms: -6 + z = 4.582575695 Solving -6 + z = 4.582575695 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = 4.582575695 + 6 Combine like terms: -6 + 6 = 0 0 + z = 4.582575695 + 6 z = 4.582575695 + 6 Combine like terms: 4.582575695 + 6 = 10.582575695 z = 10.582575695 Simplifying z = 10.582575695

Subproblem 2

z + -6 = -4.582575695 Simplifying z + -6 = -4.582575695 Reorder the terms: -6 + z = -4.582575695 Solving -6 + z = -4.582575695 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = -4.582575695 + 6 Combine like terms: -6 + 6 = 0 0 + z = -4.582575695 + 6 z = -4.582575695 + 6 Combine like terms: -4.582575695 + 6 = 1.417424305 z = 1.417424305 Simplifying z = 1.417424305

Solution

The solution to the problem is based on the solutions from the subproblems. z = {10.582575695, 1.417424305}

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