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Simplifying z2 + 2z = 64 Reorder the terms: 2z + z2 = 64 Solving 2z + z2 = 64 Solving for variable 'z'. Reorder the terms: -64 + 2z + z2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 2z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 2z + 64 + z2 = 0 + 64 Reorder the terms: -64 + 64 + 2z + z2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 2z + z2 = 0 + 64 2z + z2 = 0 + 64 Combine like terms: 0 + 64 = 64 2z + z2 = 64 The z term is 2z. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2z + 1 + z2 = 64 + 1 Reorder the terms: 1 + 2z + z2 = 64 + 1 Combine like terms: 64 + 1 = 65 1 + 2z + z2 = 65 Factor a perfect square on the left side: (z + 1)(z + 1) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (z + 1) equal to 8.062257748 and -8.062257748.Subproblem 1
z + 1 = 8.062257748 Simplifying z + 1 = 8.062257748 Reorder the terms: 1 + z = 8.062257748 Solving 1 + z = 8.062257748 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + z = 8.062257748 + -1 z = 8.062257748 + -1 Combine like terms: 8.062257748 + -1 = 7.062257748 z = 7.062257748 Simplifying z = 7.062257748Subproblem 2
z + 1 = -8.062257748 Simplifying z + 1 = -8.062257748 Reorder the terms: 1 + z = -8.062257748 Solving 1 + z = -8.062257748 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = -8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + z = -8.062257748 + -1 z = -8.062257748 + -1 Combine like terms: -8.062257748 + -1 = -9.062257748 z = -9.062257748 Simplifying z = -9.062257748Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.062257748, -9.062257748}
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