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Simplifying z2 + 4z + -33 = 0 Reorder the terms: -33 + 4z + z2 = 0 Solving -33 + 4z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 4z + 33 + z2 = 0 + 33 Reorder the terms: -33 + 33 + 4z + z2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4z + z2 = 0 + 33 4z + z2 = 0 + 33 Combine like terms: 0 + 33 = 33 4z + z2 = 33 The z term is 4z. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z + 4 + z2 = 33 + 4 Reorder the terms: 4 + 4z + z2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + 4z + z2 = 37 Factor a perfect square on the left side: (z + 2)(z + 2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (z + 2) equal to 6.08276253 and -6.08276253.Subproblem 1
z + 2 = 6.08276253 Simplifying z + 2 = 6.08276253 Reorder the terms: 2 + z = 6.08276253 Solving 2 + z = 6.08276253 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + z = 6.08276253 + -2 z = 6.08276253 + -2 Combine like terms: 6.08276253 + -2 = 4.08276253 z = 4.08276253 Simplifying z = 4.08276253Subproblem 2
z + 2 = -6.08276253 Simplifying z + 2 = -6.08276253 Reorder the terms: 2 + z = -6.08276253 Solving 2 + z = -6.08276253 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = -6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + z = -6.08276253 + -2 z = -6.08276253 + -2 Combine like terms: -6.08276253 + -2 = -8.08276253 z = -8.08276253 Simplifying z = -8.08276253Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.08276253, -8.08276253}
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