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Simplifying z2 + -3z + -360 = 0 Reorder the terms: -360 + -3z + z2 = 0 Solving -360 + -3z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + -3z + 360 + z2 = 0 + 360 Reorder the terms: -360 + 360 + -3z + z2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -3z + z2 = 0 + 360 -3z + z2 = 0 + 360 Combine like terms: 0 + 360 = 360 -3z + z2 = 360 The z term is -3z. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3z + 2.25 + z2 = 360 + 2.25 Reorder the terms: 2.25 + -3z + z2 = 360 + 2.25 Combine like terms: 360 + 2.25 = 362.25 2.25 + -3z + z2 = 362.25 Factor a perfect square on the left side: (z + -1.5)(z + -1.5) = 362.25 Calculate the square root of the right side: 19.032866311 Break this problem into two subproblems by setting (z + -1.5) equal to 19.032866311 and -19.032866311.Subproblem 1
z + -1.5 = 19.032866311 Simplifying z + -1.5 = 19.032866311 Reorder the terms: -1.5 + z = 19.032866311 Solving -1.5 + z = 19.032866311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = 19.032866311 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = 19.032866311 + 1.5 z = 19.032866311 + 1.5 Combine like terms: 19.032866311 + 1.5 = 20.532866311 z = 20.532866311 Simplifying z = 20.532866311Subproblem 2
z + -1.5 = -19.032866311 Simplifying z + -1.5 = -19.032866311 Reorder the terms: -1.5 + z = -19.032866311 Solving -1.5 + z = -19.032866311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = -19.032866311 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = -19.032866311 + 1.5 z = -19.032866311 + 1.5 Combine like terms: -19.032866311 + 1.5 = -17.532866311 z = -17.532866311 Simplifying z = -17.532866311Solution
The solution to the problem is based on the solutions from the subproblems. z = {20.532866311, -17.532866311}
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