z^2-18z=-13

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Solution for z^2-18z=-13 equation:


Simplifying
z2 + -18z = -13

Reorder the terms:
-18z + z2 = -13

Solving
-18z + z2 = -13

Solving for variable 'z'.

Reorder the terms:
13 + -18z + z2 = -13 + 13

Combine like terms: -13 + 13 = 0
13 + -18z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -18z + -13 + z2 = 0 + -13

Reorder the terms:
13 + -13 + -18z + z2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -18z + z2 = 0 + -13
-18z + z2 = 0 + -13

Combine like terms: 0 + -13 = -13
-18z + z2 = -13

The z term is -18z.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18z + 81 + z2 = -13 + 81

Reorder the terms:
81 + -18z + z2 = -13 + 81

Combine like terms: -13 + 81 = 68
81 + -18z + z2 = 68

Factor a perfect square on the left side:
(z + -9)(z + -9) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(z + -9) equal to 8.246211251 and -8.246211251.

Subproblem 1

z + -9 = 8.246211251 Simplifying z + -9 = 8.246211251 Reorder the terms: -9 + z = 8.246211251 Solving -9 + z = 8.246211251 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + z = 8.246211251 + 9 z = 8.246211251 + 9 Combine like terms: 8.246211251 + 9 = 17.246211251 z = 17.246211251 Simplifying z = 17.246211251

Subproblem 2

z + -9 = -8.246211251 Simplifying z + -9 = -8.246211251 Reorder the terms: -9 + z = -8.246211251 Solving -9 + z = -8.246211251 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = -8.246211251 + 9 Combine like terms: -9 + 9 = 0 0 + z = -8.246211251 + 9 z = -8.246211251 + 9 Combine like terms: -8.246211251 + 9 = 0.753788749 z = 0.753788749 Simplifying z = 0.753788749

Solution

The solution to the problem is based on the solutions from the subproblems. z = {17.246211251, 0.753788749}

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