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Simplifying z2 + -20z = 27 Reorder the terms: -20z + z2 = 27 Solving -20z + z2 = 27 Solving for variable 'z'. Reorder the terms: -27 + -20z + z2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -20z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -20z + 27 + z2 = 0 + 27 Reorder the terms: -27 + 27 + -20z + z2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -20z + z2 = 0 + 27 -20z + z2 = 0 + 27 Combine like terms: 0 + 27 = 27 -20z + z2 = 27 The z term is -20z. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20z + 100 + z2 = 27 + 100 Reorder the terms: 100 + -20z + z2 = 27 + 100 Combine like terms: 27 + 100 = 127 100 + -20z + z2 = 127 Factor a perfect square on the left side: (z + -10)(z + -10) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (z + -10) equal to 11.26942767 and -11.26942767.Subproblem 1
z + -10 = 11.26942767 Simplifying z + -10 = 11.26942767 Reorder the terms: -10 + z = 11.26942767 Solving -10 + z = 11.26942767 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + z = 11.26942767 + 10 Combine like terms: -10 + 10 = 0 0 + z = 11.26942767 + 10 z = 11.26942767 + 10 Combine like terms: 11.26942767 + 10 = 21.26942767 z = 21.26942767 Simplifying z = 21.26942767Subproblem 2
z + -10 = -11.26942767 Simplifying z + -10 = -11.26942767 Reorder the terms: -10 + z = -11.26942767 Solving -10 + z = -11.26942767 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + z = -11.26942767 + 10 Combine like terms: -10 + 10 = 0 0 + z = -11.26942767 + 10 z = -11.26942767 + 10 Combine like terms: -11.26942767 + 10 = -1.26942767 z = -1.26942767 Simplifying z = -1.26942767Solution
The solution to the problem is based on the solutions from the subproblems. z = {21.26942767, -1.26942767}
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