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Simplifying z2 + -18z = -19 Reorder the terms: -18z + z2 = -19 Solving -18z + z2 = -19 Solving for variable 'z'. Reorder the terms: 19 + -18z + z2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + -18z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -18z + -19 + z2 = 0 + -19 Reorder the terms: 19 + -19 + -18z + z2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -18z + z2 = 0 + -19 -18z + z2 = 0 + -19 Combine like terms: 0 + -19 = -19 -18z + z2 = -19 The z term is -18z. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18z + 81 + z2 = -19 + 81 Reorder the terms: 81 + -18z + z2 = -19 + 81 Combine like terms: -19 + 81 = 62 81 + -18z + z2 = 62 Factor a perfect square on the left side: (z + -9)(z + -9) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (z + -9) equal to 7.874007874 and -7.874007874.Subproblem 1
z + -9 = 7.874007874 Simplifying z + -9 = 7.874007874 Reorder the terms: -9 + z = 7.874007874 Solving -9 + z = 7.874007874 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 7.874007874 + 9 Combine like terms: -9 + 9 = 0 0 + z = 7.874007874 + 9 z = 7.874007874 + 9 Combine like terms: 7.874007874 + 9 = 16.874007874 z = 16.874007874 Simplifying z = 16.874007874Subproblem 2
z + -9 = -7.874007874 Simplifying z + -9 = -7.874007874 Reorder the terms: -9 + z = -7.874007874 Solving -9 + z = -7.874007874 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = -7.874007874 + 9 Combine like terms: -9 + 9 = 0 0 + z = -7.874007874 + 9 z = -7.874007874 + 9 Combine like terms: -7.874007874 + 9 = 1.125992126 z = 1.125992126 Simplifying z = 1.125992126Solution
The solution to the problem is based on the solutions from the subproblems. z = {16.874007874, 1.125992126}
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