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Simplifying z2 + 16z + 7 = 0 Reorder the terms: 7 + 16z + z2 = 0 Solving 7 + 16z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 16z + -7 + z2 = 0 + -7 Reorder the terms: 7 + -7 + 16z + z2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 16z + z2 = 0 + -7 16z + z2 = 0 + -7 Combine like terms: 0 + -7 = -7 16z + z2 = -7 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 = -7 + 64 Reorder the terms: 64 + 16z + z2 = -7 + 64 Combine like terms: -7 + 64 = 57 64 + 16z + z2 = 57 Factor a perfect square on the left side: (z + 8)(z + 8) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (z + 8) equal to 7.549834435 and -7.549834435.Subproblem 1
z + 8 = 7.549834435 Simplifying z + 8 = 7.549834435 Reorder the terms: 8 + z = 7.549834435 Solving 8 + z = 7.549834435 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 = 7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + z = 7.549834435 + -8 z = 7.549834435 + -8 Combine like terms: 7.549834435 + -8 = -0.450165565 z = -0.450165565 Simplifying z = -0.450165565Subproblem 2
z + 8 = -7.549834435 Simplifying z + 8 = -7.549834435 Reorder the terms: 8 + z = -7.549834435 Solving 8 + z = -7.549834435 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 = -7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + z = -7.549834435 + -8 z = -7.549834435 + -8 Combine like terms: -7.549834435 + -8 = -15.549834435 z = -15.549834435 Simplifying z = -15.549834435Solution
The solution to the problem is based on the solutions from the subproblems. z = {-0.450165565, -15.549834435}
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