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Simplifying z2 + -15z + -156 = 0 Reorder the terms: -156 + -15z + z2 = 0 Solving -156 + -15z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + -15z + 156 + z2 = 0 + 156 Reorder the terms: -156 + 156 + -15z + z2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + -15z + z2 = 0 + 156 -15z + z2 = 0 + 156 Combine like terms: 0 + 156 = 156 -15z + z2 = 156 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 = 156 + 56.25 Reorder the terms: 56.25 + -15z + z2 = 156 + 56.25 Combine like terms: 156 + 56.25 = 212.25 56.25 + -15z + z2 = 212.25 Factor a perfect square on the left side: (z + -7.5)(z + -7.5) = 212.25 Calculate the square root of the right side: 14.568802284 Break this problem into two subproblems by setting (z + -7.5) equal to 14.568802284 and -14.568802284.Subproblem 1
z + -7.5 = 14.568802284 Simplifying z + -7.5 = 14.568802284 Reorder the terms: -7.5 + z = 14.568802284 Solving -7.5 + z = 14.568802284 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 = 14.568802284 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = 14.568802284 + 7.5 z = 14.568802284 + 7.5 Combine like terms: 14.568802284 + 7.5 = 22.068802284 z = 22.068802284 Simplifying z = 22.068802284Subproblem 2
z + -7.5 = -14.568802284 Simplifying z + -7.5 = -14.568802284 Reorder the terms: -7.5 + z = -14.568802284 Solving -7.5 + z = -14.568802284 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 = -14.568802284 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + z = -14.568802284 + 7.5 z = -14.568802284 + 7.5 Combine like terms: -14.568802284 + 7.5 = -7.068802284 z = -7.068802284 Simplifying z = -7.068802284Solution
The solution to the problem is based on the solutions from the subproblems. z = {22.068802284, -7.068802284}
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