z^2-13z=36

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Solution for z^2-13z=36 equation:


Simplifying
z2 + -13z = 36

Reorder the terms:
-13z + z2 = 36

Solving
-13z + z2 = 36

Solving for variable 'z'.

Reorder the terms:
-36 + -13z + z2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -13z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -13z + 36 + z2 = 0 + 36

Reorder the terms:
-36 + 36 + -13z + z2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -13z + z2 = 0 + 36
-13z + z2 = 0 + 36

Combine like terms: 0 + 36 = 36
-13z + z2 = 36

The z term is -13z.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13z + 42.25 + z2 = 36 + 42.25

Reorder the terms:
42.25 + -13z + z2 = 36 + 42.25

Combine like terms: 36 + 42.25 = 78.25
42.25 + -13z + z2 = 78.25

Factor a perfect square on the left side:
(z + -6.5)(z + -6.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(z + -6.5) equal to 8.845903006 and -8.845903006.

Subproblem 1

z + -6.5 = 8.845903006 Simplifying z + -6.5 = 8.845903006 Reorder the terms: -6.5 + z = 8.845903006 Solving -6.5 + z = 8.845903006 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + z = 8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + z = 8.845903006 + 6.5 z = 8.845903006 + 6.5 Combine like terms: 8.845903006 + 6.5 = 15.345903006 z = 15.345903006 Simplifying z = 15.345903006

Subproblem 2

z + -6.5 = -8.845903006 Simplifying z + -6.5 = -8.845903006 Reorder the terms: -6.5 + z = -8.845903006 Solving -6.5 + z = -8.845903006 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + z = -8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + z = -8.845903006 + 6.5 z = -8.845903006 + 6.5 Combine like terms: -8.845903006 + 6.5 = -2.345903006 z = -2.345903006 Simplifying z = -2.345903006

Solution

The solution to the problem is based on the solutions from the subproblems. z = {15.345903006, -2.345903006}

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