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Simplifying z2 + -14z = -17 Reorder the terms: -14z + z2 = -17 Solving -14z + z2 = -17 Solving for variable 'z'. Reorder the terms: 17 + -14z + z2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + -14z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -14z + -17 + z2 = 0 + -17 Reorder the terms: 17 + -17 + -14z + z2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -14z + z2 = 0 + -17 -14z + z2 = 0 + -17 Combine like terms: 0 + -17 = -17 -14z + z2 = -17 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 = -17 + 49 Reorder the terms: 49 + -14z + z2 = -17 + 49 Combine like terms: -17 + 49 = 32 49 + -14z + z2 = 32 Factor a perfect square on the left side: (z + -7)(z + -7) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (z + -7) equal to 5.656854249 and -5.656854249.Subproblem 1
z + -7 = 5.656854249 Simplifying z + -7 = 5.656854249 Reorder the terms: -7 + z = 5.656854249 Solving -7 + z = 5.656854249 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 = 5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + z = 5.656854249 + 7 z = 5.656854249 + 7 Combine like terms: 5.656854249 + 7 = 12.656854249 z = 12.656854249 Simplifying z = 12.656854249Subproblem 2
z + -7 = -5.656854249 Simplifying z + -7 = -5.656854249 Reorder the terms: -7 + z = -5.656854249 Solving -7 + z = -5.656854249 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 = -5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + z = -5.656854249 + 7 z = -5.656854249 + 7 Combine like terms: -5.656854249 + 7 = 1.343145751 z = 1.343145751 Simplifying z = 1.343145751Solution
The solution to the problem is based on the solutions from the subproblems. z = {12.656854249, 1.343145751}
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