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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 = 71 64 + 16z + z2 = 71 Factor a perfect square on the left side: (z + 8)(z + 8) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (z + 8) equal to 8.426149773 and -8.426149773.Subproblem 1
z + 8 = 8.426149773 Simplifying z + 8 = 8.426149773 Reorder the terms: 8 + z = 8.426149773 Solving 8 + z = 8.426149773 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 = 8.426149773 + -8 Combine like terms: 8 + -8 = 0 0 + z = 8.426149773 + -8 z = 8.426149773 + -8 Combine like terms: 8.426149773 + -8 = 0.426149773 z = 0.426149773 Simplifying z = 0.426149773Subproblem 2
z + 8 = -8.426149773 Simplifying z + 8 = -8.426149773 Reorder the terms: 8 + z = -8.426149773 Solving 8 + z = -8.426149773 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 = -8.426149773 + -8 Combine like terms: 8 + -8 = 0 0 + z = -8.426149773 + -8 z = -8.426149773 + -8 Combine like terms: -8.426149773 + -8 = -16.426149773 z = -16.426149773 Simplifying z = -16.426149773Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.426149773, -16.426149773}
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