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Simplifying z2 + -16z = -11 Reorder the terms: -16z + z2 = -11 Solving -16z + z2 = -11 Solving for variable 'z'. Reorder the terms: 11 + -16z + z2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -16z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -16z + -11 + z2 = 0 + -11 Reorder the terms: 11 + -11 + -16z + z2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -16z + z2 = 0 + -11 -16z + z2 = 0 + -11 Combine like terms: 0 + -11 = -11 -16z + z2 = -11 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 = -11 + 64 Reorder the terms: 64 + -16z + z2 = -11 + 64 Combine like terms: -11 + 64 = 53 64 + -16z + z2 = 53 Factor a perfect square on the left side: (z + -8)(z + -8) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (z + -8) equal to 7.280109889 and -7.280109889.Subproblem 1
z + -8 = 7.280109889 Simplifying z + -8 = 7.280109889 Reorder the terms: -8 + z = 7.280109889 Solving -8 + z = 7.280109889 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 = 7.280109889 + 8 Combine like terms: -8 + 8 = 0 0 + z = 7.280109889 + 8 z = 7.280109889 + 8 Combine like terms: 7.280109889 + 8 = 15.280109889 z = 15.280109889 Simplifying z = 15.280109889Subproblem 2
z + -8 = -7.280109889 Simplifying z + -8 = -7.280109889 Reorder the terms: -8 + z = -7.280109889 Solving -8 + z = -7.280109889 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 = -7.280109889 + 8 Combine like terms: -8 + 8 = 0 0 + z = -7.280109889 + 8 z = -7.280109889 + 8 Combine like terms: -7.280109889 + 8 = 0.719890111 z = 0.719890111 Simplifying z = 0.719890111Solution
The solution to the problem is based on the solutions from the subproblems. z = {15.280109889, 0.719890111}
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