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Simplifying z2 = 15z + 36 Reorder the terms: z2 = 36 + 15z Solving z2 = 36 + 15z Solving for variable 'z'. Reorder the terms: -36 + -15z + z2 = 36 + 15z + -36 + -15z Reorder the terms: -36 + -15z + z2 = 36 + -36 + 15z + -15z Combine like terms: 36 + -36 = 0 -36 + -15z + z2 = 0 + 15z + -15z -36 + -15z + z2 = 15z + -15z Combine like terms: 15z + -15z = 0 -36 + -15z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -15z + 36 + z2 = 0 + 36 Reorder the terms: -36 + 36 + -15z + z2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -15z + z2 = 0 + 36 -15z + z2 = 0 + 36 Combine like terms: 0 + 36 = 36 -15z + z2 = 36 The z term is -15z. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15z + 56.25 + z2 = 36 + 56.25 Reorder the terms: 56.25 + -15z + z2 = 36 + 56.25 Combine like terms: 36 + 56.25 = 92.25 56.25 + -15z + z2 = 92.25 Factor a perfect square on the left side: (z + -7.5)(z + -7.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (z + -7.5) equal to 9.604686356 and -9.604686356.Subproblem 1
z + -7.5 = 9.604686356 Simplifying z + -7.5 = 9.604686356 Reorder the terms: -7.5 + z = 9.604686356 Solving -7.5 + z = 9.604686356 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + z = 9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = 9.604686356 + 7.5 z = 9.604686356 + 7.5 Combine like terms: 9.604686356 + 7.5 = 17.104686356 z = 17.104686356 Simplifying z = 17.104686356Subproblem 2
z + -7.5 = -9.604686356 Simplifying z + -7.5 = -9.604686356 Reorder the terms: -7.5 + z = -9.604686356 Solving -7.5 + z = -9.604686356 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + z = -9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = -9.604686356 + 7.5 z = -9.604686356 + 7.5 Combine like terms: -9.604686356 + 7.5 = -2.104686356 z = -2.104686356 Simplifying z = -2.104686356Solution
The solution to the problem is based on the solutions from the subproblems. z = {17.104686356, -2.104686356}
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