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Simplifying z2 + -30z = -43 Reorder the terms: -30z + z2 = -43 Solving -30z + z2 = -43 Solving for variable 'z'. Reorder the terms: 43 + -30z + z2 = -43 + 43 Combine like terms: -43 + 43 = 0 43 + -30z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -30z + -43 + z2 = 0 + -43 Reorder the terms: 43 + -43 + -30z + z2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -30z + z2 = 0 + -43 -30z + z2 = 0 + -43 Combine like terms: 0 + -43 = -43 -30z + z2 = -43 The z term is -30z. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30z + 225 + z2 = -43 + 225 Reorder the terms: 225 + -30z + z2 = -43 + 225 Combine like terms: -43 + 225 = 182 225 + -30z + z2 = 182 Factor a perfect square on the left side: (z + -15)(z + -15) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (z + -15) equal to 13.490737563 and -13.490737563.Subproblem 1
z + -15 = 13.490737563 Simplifying z + -15 = 13.490737563 Reorder the terms: -15 + z = 13.490737563 Solving -15 + z = 13.490737563 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + z = 13.490737563 + 15 Combine like terms: -15 + 15 = 0 0 + z = 13.490737563 + 15 z = 13.490737563 + 15 Combine like terms: 13.490737563 + 15 = 28.490737563 z = 28.490737563 Simplifying z = 28.490737563Subproblem 2
z + -15 = -13.490737563 Simplifying z + -15 = -13.490737563 Reorder the terms: -15 + z = -13.490737563 Solving -15 + z = -13.490737563 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + z = -13.490737563 + 15 Combine like terms: -15 + 15 = 0 0 + z = -13.490737563 + 15 z = -13.490737563 + 15 Combine like terms: -13.490737563 + 15 = 1.509262437 z = 1.509262437 Simplifying z = 1.509262437Solution
The solution to the problem is based on the solutions from the subproblems. z = {28.490737563, 1.509262437}
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