z^2-12z=-13

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Solution for z^2-12z=-13 equation:


Simplifying
z2 + -12z = -13

Reorder the terms:
-12z + z2 = -13

Solving
-12z + z2 = -13

Solving for variable 'z'.

Reorder the terms:
13 + -12z + z2 = -13 + 13

Combine like terms: -13 + 13 = 0
13 + -12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -12z + -13 + z2 = 0 + -13

Reorder the terms:
13 + -13 + -12z + z2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -12z + z2 = 0 + -13
-12z + z2 = 0 + -13

Combine like terms: 0 + -13 = -13
-12z + z2 = -13

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 = -13 + 36

Reorder the terms:
36 + -12z + z2 = -13 + 36

Combine like terms: -13 + 36 = 23
36 + -12z + z2 = 23

Factor a perfect square on the left side:
(z + -6)(z + -6) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(z + -6) equal to 4.795831523 and -4.795831523.

Subproblem 1

z + -6 = 4.795831523 Simplifying z + -6 = 4.795831523 Reorder the terms: -6 + z = 4.795831523 Solving -6 + z = 4.795831523 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 = 4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + z = 4.795831523 + 6 z = 4.795831523 + 6 Combine like terms: 4.795831523 + 6 = 10.795831523 z = 10.795831523 Simplifying z = 10.795831523

Subproblem 2

z + -6 = -4.795831523 Simplifying z + -6 = -4.795831523 Reorder the terms: -6 + z = -4.795831523 Solving -6 + z = -4.795831523 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 = -4.795831523 + 6 Combine like terms: -6 + 6 = 0 0 + z = -4.795831523 + 6 z = -4.795831523 + 6 Combine like terms: -4.795831523 + 6 = 1.204168477 z = 1.204168477 Simplifying z = 1.204168477

Solution

The solution to the problem is based on the solutions from the subproblems. z = {10.795831523, 1.204168477}

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