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Simplifying -2z2 + -38z = -16 Reorder the terms: -38z + -2z2 = -16 Solving -38z + -2z2 = -16 Solving for variable 'z'. Reorder the terms: 16 + -38z + -2z2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + -38z + -2z2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -19z + -1z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -19z + -1z2)' equal to zero and attempt to solve: Simplifying 8 + -19z + -1z2 = 0 Solving 8 + -19z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 19z + z2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 19z + 8 + z2 = 0 + 8 Reorder the terms: -8 + 8 + 19z + z2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 19z + z2 = 0 + 8 19z + z2 = 0 + 8 Combine like terms: 0 + 8 = 8 19z + z2 = 8 The z term is 19z. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19z + 90.25 + z2 = 8 + 90.25 Reorder the terms: 90.25 + 19z + z2 = 8 + 90.25 Combine like terms: 8 + 90.25 = 98.25 90.25 + 19z + z2 = 98.25 Factor a perfect square on the left side: (z + 9.5)(z + 9.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (z + 9.5) equal to 9.912113801 and -9.912113801.Subproblem 1
z + 9.5 = 9.912113801 Simplifying z + 9.5 = 9.912113801 Reorder the terms: 9.5 + z = 9.912113801 Solving 9.5 + z = 9.912113801 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + z = 9.912113801 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + z = 9.912113801 + -9.5 z = 9.912113801 + -9.5 Combine like terms: 9.912113801 + -9.5 = 0.412113801 z = 0.412113801 Simplifying z = 0.412113801Subproblem 2
z + 9.5 = -9.912113801 Simplifying z + 9.5 = -9.912113801 Reorder the terms: 9.5 + z = -9.912113801 Solving 9.5 + z = -9.912113801 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + z = -9.912113801 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + z = -9.912113801 + -9.5 z = -9.912113801 + -9.5 Combine like terms: -9.912113801 + -9.5 = -19.412113801 z = -19.412113801 Simplifying z = -19.412113801Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.412113801, -19.412113801}Solution
z = {0.412113801, -19.412113801}
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