18z+45=z^2

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Solution for 18z+45=z^2 equation:


Simplifying
18z + 45 = z2

Reorder the terms:
45 + 18z = z2

Solving
45 + 18z = z2

Solving for variable 'z'.

Combine like terms: z2 + -1z2 = 0
45 + 18z + -1z2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-45 + -18z + z2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -18z + 45 + z2 = 0 + 45

Reorder the terms:
-45 + 45 + -18z + z2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -18z + z2 = 0 + 45
-18z + z2 = 0 + 45

Combine like terms: 0 + 45 = 45
-18z + z2 = 45

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 = 45 + 81

Reorder the terms:
81 + -18z + z2 = 45 + 81

Combine like terms: 45 + 81 = 126
81 + -18z + z2 = 126

Factor a perfect square on the left side:
(z + -9)(z + -9) = 126

Calculate the square root of the right side: 11.22497216

Break this problem into two subproblems by setting 
(z + -9) equal to 11.22497216 and -11.22497216.

Subproblem 1

z + -9 = 11.22497216 Simplifying z + -9 = 11.22497216 Reorder the terms: -9 + z = 11.22497216 Solving -9 + z = 11.22497216 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 = 11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + z = 11.22497216 + 9 z = 11.22497216 + 9 Combine like terms: 11.22497216 + 9 = 20.22497216 z = 20.22497216 Simplifying z = 20.22497216

Subproblem 2

z + -9 = -11.22497216 Simplifying z + -9 = -11.22497216 Reorder the terms: -9 + z = -11.22497216 Solving -9 + z = -11.22497216 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 = -11.22497216 + 9 Combine like terms: -9 + 9 = 0 0 + z = -11.22497216 + 9 z = -11.22497216 + 9 Combine like terms: -11.22497216 + 9 = -2.22497216 z = -2.22497216 Simplifying z = -2.22497216

Solution

The solution to the problem is based on the solutions from the subproblems. z = {20.22497216, -2.22497216}

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