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Simplifying z2 + -15z + 12 = 0 Reorder the terms: 12 + -15z + z2 = 0 Solving 12 + -15z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -15z + -12 + z2 = 0 + -12 Reorder the terms: 12 + -12 + -15z + z2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -15z + z2 = 0 + -12 -15z + z2 = 0 + -12 Combine like terms: 0 + -12 = -12 -15z + z2 = -12 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 = -12 + 56.25 Reorder the terms: 56.25 + -15z + z2 = -12 + 56.25 Combine like terms: -12 + 56.25 = 44.25 56.25 + -15z + z2 = 44.25 Factor a perfect square on the left side: (z + -7.5)(z + -7.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (z + -7.5) equal to 6.652067348 and -6.652067348.Subproblem 1
z + -7.5 = 6.652067348 Simplifying z + -7.5 = 6.652067348 Reorder the terms: -7.5 + z = 6.652067348 Solving -7.5 + z = 6.652067348 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 = 6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = 6.652067348 + 7.5 z = 6.652067348 + 7.5 Combine like terms: 6.652067348 + 7.5 = 14.152067348 z = 14.152067348 Simplifying z = 14.152067348Subproblem 2
z + -7.5 = -6.652067348 Simplifying z + -7.5 = -6.652067348 Reorder the terms: -7.5 + z = -6.652067348 Solving -7.5 + z = -6.652067348 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 = -6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = -6.652067348 + 7.5 z = -6.652067348 + 7.5 Combine like terms: -6.652067348 + 7.5 = 0.847932652 z = 0.847932652 Simplifying z = 0.847932652Solution
The solution to the problem is based on the solutions from the subproblems. z = {14.152067348, 0.847932652}
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