z^2-18z=7

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Solution for z^2-18z=7 equation:


Simplifying
z2 + -18z = 7

Reorder the terms:
-18z + z2 = 7

Solving
-18z + z2 = 7

Solving for variable 'z'.

Reorder the terms:
-7 + -18z + z2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -18z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -18z + 7 + z2 = 0 + 7

Reorder the terms:
-7 + 7 + -18z + z2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -18z + z2 = 0 + 7
-18z + z2 = 0 + 7

Combine like terms: 0 + 7 = 7
-18z + z2 = 7

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 = 7 + 81

Reorder the terms:
81 + -18z + z2 = 7 + 81

Combine like terms: 7 + 81 = 88
81 + -18z + z2 = 88

Factor a perfect square on the left side:
(z + -9)(z + -9) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(z + -9) equal to 9.38083152 and -9.38083152.

Subproblem 1

z + -9 = 9.38083152 Simplifying z + -9 = 9.38083152 Reorder the terms: -9 + z = 9.38083152 Solving -9 + z = 9.38083152 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 = 9.38083152 + 9 Combine like terms: -9 + 9 = 0 0 + z = 9.38083152 + 9 z = 9.38083152 + 9 Combine like terms: 9.38083152 + 9 = 18.38083152 z = 18.38083152 Simplifying z = 18.38083152

Subproblem 2

z + -9 = -9.38083152 Simplifying z + -9 = -9.38083152 Reorder the terms: -9 + z = -9.38083152 Solving -9 + z = -9.38083152 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 = -9.38083152 + 9 Combine like terms: -9 + 9 = 0 0 + z = -9.38083152 + 9 z = -9.38083152 + 9 Combine like terms: -9.38083152 + 9 = -0.38083152 z = -0.38083152 Simplifying z = -0.38083152

Solution

The solution to the problem is based on the solutions from the subproblems. z = {18.38083152, -0.38083152}

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