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Simplifying z2 + -14z = -15 Reorder the terms: -14z + z2 = -15 Solving -14z + z2 = -15 Solving for variable 'z'. Reorder the terms: 15 + -14z + z2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -14z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -14z + -15 + z2 = 0 + -15 Reorder the terms: 15 + -15 + -14z + z2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -14z + z2 = 0 + -15 -14z + z2 = 0 + -15 Combine like terms: 0 + -15 = -15 -14z + z2 = -15 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 = -15 + 49 Reorder the terms: 49 + -14z + z2 = -15 + 49 Combine like terms: -15 + 49 = 34 49 + -14z + z2 = 34 Factor a perfect square on the left side: (z + -7)(z + -7) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (z + -7) equal to 5.830951895 and -5.830951895.Subproblem 1
z + -7 = 5.830951895 Simplifying z + -7 = 5.830951895 Reorder the terms: -7 + z = 5.830951895 Solving -7 + z = 5.830951895 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 = 5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + z = 5.830951895 + 7 z = 5.830951895 + 7 Combine like terms: 5.830951895 + 7 = 12.830951895 z = 12.830951895 Simplifying z = 12.830951895Subproblem 2
z + -7 = -5.830951895 Simplifying z + -7 = -5.830951895 Reorder the terms: -7 + z = -5.830951895 Solving -7 + z = -5.830951895 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 = -5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + z = -5.830951895 + 7 z = -5.830951895 + 7 Combine like terms: -5.830951895 + 7 = 1.169048105 z = 1.169048105 Simplifying z = 1.169048105Solution
The solution to the problem is based on the solutions from the subproblems. z = {12.830951895, 1.169048105}
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