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Simplifying z2 + -16z + 9 = 0 Reorder the terms: 9 + -16z + z2 = 0 Solving 9 + -16z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -16z + -9 + z2 = 0 + -9 Reorder the terms: 9 + -9 + -16z + z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16z + z2 = 0 + -9 -16z + z2 = 0 + -9 Combine like terms: 0 + -9 = -9 -16z + z2 = -9 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 = -9 + 64 Reorder the terms: 64 + -16z + z2 = -9 + 64 Combine like terms: -9 + 64 = 55 64 + -16z + z2 = 55 Factor a perfect square on the left side: (z + -8)(z + -8) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (z + -8) equal to 7.416198487 and -7.416198487.Subproblem 1
z + -8 = 7.416198487 Simplifying z + -8 = 7.416198487 Reorder the terms: -8 + z = 7.416198487 Solving -8 + z = 7.416198487 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 = 7.416198487 + 8 Combine like terms: -8 + 8 = 0 0 + z = 7.416198487 + 8 z = 7.416198487 + 8 Combine like terms: 7.416198487 + 8 = 15.416198487 z = 15.416198487 Simplifying z = 15.416198487Subproblem 2
z + -8 = -7.416198487 Simplifying z + -8 = -7.416198487 Reorder the terms: -8 + z = -7.416198487 Solving -8 + z = -7.416198487 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 = -7.416198487 + 8 Combine like terms: -8 + 8 = 0 0 + z = -7.416198487 + 8 z = -7.416198487 + 8 Combine like terms: -7.416198487 + 8 = 0.583801513 z = 0.583801513 Simplifying z = 0.583801513Solution
The solution to the problem is based on the solutions from the subproblems. z = {15.416198487, 0.583801513}
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