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Simplifying z2 + -12z + -270 = 0 Reorder the terms: -270 + -12z + z2 = 0 Solving -270 + -12z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + -12z + 270 + z2 = 0 + 270 Reorder the terms: -270 + 270 + -12z + z2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -12z + z2 = 0 + 270 -12z + z2 = 0 + 270 Combine like terms: 0 + 270 = 270 -12z + z2 = 270 The z term is -12z. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12z + 36 + z2 = 270 + 36 Reorder the terms: 36 + -12z + z2 = 270 + 36 Combine like terms: 270 + 36 = 306 36 + -12z + z2 = 306 Factor a perfect square on the left side: (z + -6)(z + -6) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (z + -6) equal to 17.492855685 and -17.492855685.Subproblem 1
z + -6 = 17.492855685 Simplifying z + -6 = 17.492855685 Reorder the terms: -6 + z = 17.492855685 Solving -6 + z = 17.492855685 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = 17.492855685 + 6 Combine like terms: -6 + 6 = 0 0 + z = 17.492855685 + 6 z = 17.492855685 + 6 Combine like terms: 17.492855685 + 6 = 23.492855685 z = 23.492855685 Simplifying z = 23.492855685Subproblem 2
z + -6 = -17.492855685 Simplifying z + -6 = -17.492855685 Reorder the terms: -6 + z = -17.492855685 Solving -6 + z = -17.492855685 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = -17.492855685 + 6 Combine like terms: -6 + 6 = 0 0 + z = -17.492855685 + 6 z = -17.492855685 + 6 Combine like terms: -17.492855685 + 6 = -11.492855685 z = -11.492855685 Simplifying z = -11.492855685Solution
The solution to the problem is based on the solutions from the subproblems. z = {23.492855685, -11.492855685}
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