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Simplifying z2 + 4z = 39 Reorder the terms: 4z + z2 = 39 Solving 4z + z2 = 39 Solving for variable 'z'. Reorder the terms: -39 + 4z + z2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + 4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 4z + 39 + z2 = 0 + 39 Reorder the terms: -39 + 39 + 4z + z2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 4z + z2 = 0 + 39 4z + z2 = 0 + 39 Combine like terms: 0 + 39 = 39 4z + z2 = 39 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 = 39 + 4 Reorder the terms: 4 + 4z + z2 = 39 + 4 Combine like terms: 39 + 4 = 43 4 + 4z + z2 = 43 Factor a perfect square on the left side: (z + 2)(z + 2) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (z + 2) equal to 6.557438524 and -6.557438524.Subproblem 1
z + 2 = 6.557438524 Simplifying z + 2 = 6.557438524 Reorder the terms: 2 + z = 6.557438524 Solving 2 + z = 6.557438524 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 = 6.557438524 + -2 Combine like terms: 2 + -2 = 0 0 + z = 6.557438524 + -2 z = 6.557438524 + -2 Combine like terms: 6.557438524 + -2 = 4.557438524 z = 4.557438524 Simplifying z = 4.557438524Subproblem 2
z + 2 = -6.557438524 Simplifying z + 2 = -6.557438524 Reorder the terms: 2 + z = -6.557438524 Solving 2 + z = -6.557438524 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 = -6.557438524 + -2 Combine like terms: 2 + -2 = 0 0 + z = -6.557438524 + -2 z = -6.557438524 + -2 Combine like terms: -6.557438524 + -2 = -8.557438524 z = -8.557438524 Simplifying z = -8.557438524Solution
The solution to the problem is based on the solutions from the subproblems. z = {4.557438524, -8.557438524}
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