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Simplifying z2 + -14z + 42 = 0 Reorder the terms: 42 + -14z + z2 = 0 Solving 42 + -14z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -14z + -42 + z2 = 0 + -42 Reorder the terms: 42 + -42 + -14z + z2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -14z + z2 = 0 + -42 -14z + z2 = 0 + -42 Combine like terms: 0 + -42 = -42 -14z + z2 = -42 The z term is -14z. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14z + 49 + z2 = -42 + 49 Reorder the terms: 49 + -14z + z2 = -42 + 49 Combine like terms: -42 + 49 = 7 49 + -14z + z2 = 7 Factor a perfect square on the left side: (z + -7)(z + -7) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (z + -7) equal to 2.645751311 and -2.645751311.Subproblem 1
z + -7 = 2.645751311 Simplifying z + -7 = 2.645751311 Reorder the terms: -7 + z = 2.645751311 Solving -7 + z = 2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = 2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + z = 2.645751311 + 7 z = 2.645751311 + 7 Combine like terms: 2.645751311 + 7 = 9.645751311 z = 9.645751311 Simplifying z = 9.645751311Subproblem 2
z + -7 = -2.645751311 Simplifying z + -7 = -2.645751311 Reorder the terms: -7 + z = -2.645751311 Solving -7 + z = -2.645751311 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = -2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + z = -2.645751311 + 7 z = -2.645751311 + 7 Combine like terms: -2.645751311 + 7 = 4.354248689 z = 4.354248689 Simplifying z = 4.354248689Solution
The solution to the problem is based on the solutions from the subproblems. z = {9.645751311, 4.354248689}
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