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Simplifying z2 + -16z = -10 Reorder the terms: -16z + z2 = -10 Solving -16z + z2 = -10 Solving for variable 'z'. Reorder the terms: 10 + -16z + z2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -16z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -16z + -10 + z2 = 0 + -10 Reorder the terms: 10 + -10 + -16z + z2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -16z + z2 = 0 + -10 -16z + z2 = 0 + -10 Combine like terms: 0 + -10 = -10 -16z + z2 = -10 The z term is -16z. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16z + 64 + z2 = -10 + 64 Reorder the terms: 64 + -16z + z2 = -10 + 64 Combine like terms: -10 + 64 = 54 64 + -16z + z2 = 54 Factor a perfect square on the left side: (z + -8)(z + -8) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (z + -8) equal to 7.348469228 and -7.348469228.Subproblem 1
z + -8 = 7.348469228 Simplifying z + -8 = 7.348469228 Reorder the terms: -8 + z = 7.348469228 Solving -8 + z = 7.348469228 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = 7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + z = 7.348469228 + 8 z = 7.348469228 + 8 Combine like terms: 7.348469228 + 8 = 15.348469228 z = 15.348469228 Simplifying z = 15.348469228Subproblem 2
z + -8 = -7.348469228 Simplifying z + -8 = -7.348469228 Reorder the terms: -8 + z = -7.348469228 Solving -8 + z = -7.348469228 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + z = -7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + z = -7.348469228 + 8 z = -7.348469228 + 8 Combine like terms: -7.348469228 + 8 = 0.651530772 z = 0.651530772 Simplifying z = 0.651530772Solution
The solution to the problem is based on the solutions from the subproblems. z = {15.348469228, 0.651530772}
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