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Simplifying z2 + 14z + 39 = 0 Reorder the terms: 39 + 14z + z2 = 0 Solving 39 + 14z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 14z + -39 + z2 = 0 + -39 Reorder the terms: 39 + -39 + 14z + z2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 14z + z2 = 0 + -39 14z + z2 = 0 + -39 Combine like terms: 0 + -39 = -39 14z + z2 = -39 The z term is 14z. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14z + 49 + z2 = -39 + 49 Reorder the terms: 49 + 14z + z2 = -39 + 49 Combine like terms: -39 + 49 = 10 49 + 14z + z2 = 10 Factor a perfect square on the left side: (z + 7)(z + 7) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (z + 7) equal to 3.16227766 and -3.16227766.Subproblem 1
z + 7 = 3.16227766 Simplifying z + 7 = 3.16227766 Reorder the terms: 7 + z = 3.16227766 Solving 7 + z = 3.16227766 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + z = 3.16227766 + -7 z = 3.16227766 + -7 Combine like terms: 3.16227766 + -7 = -3.83772234 z = -3.83772234 Simplifying z = -3.83772234Subproblem 2
z + 7 = -3.16227766 Simplifying z + 7 = -3.16227766 Reorder the terms: 7 + z = -3.16227766 Solving 7 + z = -3.16227766 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = -3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + z = -3.16227766 + -7 z = -3.16227766 + -7 Combine like terms: -3.16227766 + -7 = -10.16227766 z = -10.16227766 Simplifying z = -10.16227766Solution
The solution to the problem is based on the solutions from the subproblems. z = {-3.83772234, -10.16227766}
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