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Simplifying z2 = 18 + z Solving z2 = 18 + z Solving for variable 'z'. Reorder the terms: -18 + -1z + z2 = 18 + z + -18 + -1z Reorder the terms: -18 + -1z + z2 = 18 + -18 + z + -1z Combine like terms: 18 + -18 = 0 -18 + -1z + z2 = 0 + z + -1z -18 + -1z + z2 = z + -1z Combine like terms: z + -1z = 0 -18 + -1z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -1z + 18 + z2 = 0 + 18 Reorder the terms: -18 + 18 + -1z + z2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1z + z2 = 0 + 18 -1z + z2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1z + z2 = 18 The z term is -1z. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1z + 0.25 + z2 = 18 + 0.25 Reorder the terms: 0.25 + -1z + z2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + -1z + z2 = 18.25 Factor a perfect square on the left side: (z + -0.5)(z + -0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (z + -0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
z + -0.5 = 4.272001873 Simplifying z + -0.5 = 4.272001873 Reorder the terms: -0.5 + z = 4.272001873 Solving -0.5 + z = 4.272001873 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 4.272001873 + 0.5 z = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 z = 4.772001873 Simplifying z = 4.772001873Subproblem 2
z + -0.5 = -4.272001873 Simplifying z + -0.5 = -4.272001873 Reorder the terms: -0.5 + z = -4.272001873 Solving -0.5 + z = -4.272001873 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + z = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -4.272001873 + 0.5 z = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 z = -3.772001873 Simplifying z = -3.772001873Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.772001873, -3.772001873}
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