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Simplifying 2z2 + 36z + 98 = 0 Reorder the terms: 98 + 36z + 2z2 = 0 Solving 98 + 36z + 2z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2'. 2(49 + 18z + z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + 18z + z2)' equal to zero and attempt to solve: Simplifying 49 + 18z + z2 = 0 Solving 49 + 18z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + 18z + -49 + z2 = 0 + -49 Reorder the terms: 49 + -49 + 18z + z2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + 18z + z2 = 0 + -49 18z + z2 = 0 + -49 Combine like terms: 0 + -49 = -49 18z + z2 = -49 The z term is 18z. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18z + 81 + z2 = -49 + 81 Reorder the terms: 81 + 18z + z2 = -49 + 81 Combine like terms: -49 + 81 = 32 81 + 18z + z2 = 32 Factor a perfect square on the left side: (z + 9)(z + 9) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (z + 9) equal to 5.656854249 and -5.656854249.Subproblem 1
z + 9 = 5.656854249 Simplifying z + 9 = 5.656854249 Reorder the terms: 9 + z = 5.656854249 Solving 9 + z = 5.656854249 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = 5.656854249 + -9 Combine like terms: 9 + -9 = 0 0 + z = 5.656854249 + -9 z = 5.656854249 + -9 Combine like terms: 5.656854249 + -9 = -3.343145751 z = -3.343145751 Simplifying z = -3.343145751Subproblem 2
z + 9 = -5.656854249 Simplifying z + 9 = -5.656854249 Reorder the terms: 9 + z = -5.656854249 Solving 9 + z = -5.656854249 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + z = -5.656854249 + -9 Combine like terms: 9 + -9 = 0 0 + z = -5.656854249 + -9 z = -5.656854249 + -9 Combine like terms: -5.656854249 + -9 = -14.656854249 z = -14.656854249 Simplifying z = -14.656854249Solution
The solution to the problem is based on the solutions from the subproblems. z = {-3.343145751, -14.656854249}Solution
z = {-3.343145751, -14.656854249}
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