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Simplifying z2 + -19z = 56 Reorder the terms: -19z + z2 = 56 Solving -19z + z2 = 56 Solving for variable 'z'. Reorder the terms: -56 + -19z + z2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -19z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -19z + 56 + z2 = 0 + 56 Reorder the terms: -56 + 56 + -19z + z2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -19z + z2 = 0 + 56 -19z + z2 = 0 + 56 Combine like terms: 0 + 56 = 56 -19z + z2 = 56 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 = 56 + 90.25 Reorder the terms: 90.25 + -19z + z2 = 56 + 90.25 Combine like terms: 56 + 90.25 = 146.25 90.25 + -19z + z2 = 146.25 Factor a perfect square on the left side: (z + -9.5)(z + -9.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (z + -9.5) equal to 12.093386622 and -12.093386622.Subproblem 1
z + -9.5 = 12.093386622 Simplifying z + -9.5 = 12.093386622 Reorder the terms: -9.5 + z = 12.093386622 Solving -9.5 + z = 12.093386622 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 = 12.093386622 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + z = 12.093386622 + 9.5 z = 12.093386622 + 9.5 Combine like terms: 12.093386622 + 9.5 = 21.593386622 z = 21.593386622 Simplifying z = 21.593386622Subproblem 2
z + -9.5 = -12.093386622 Simplifying z + -9.5 = -12.093386622 Reorder the terms: -9.5 + z = -12.093386622 Solving -9.5 + z = -12.093386622 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 = -12.093386622 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + z = -12.093386622 + 9.5 z = -12.093386622 + 9.5 Combine like terms: -12.093386622 + 9.5 = -2.593386622 z = -2.593386622 Simplifying z = -2.593386622Solution
The solution to the problem is based on the solutions from the subproblems. z = {21.593386622, -2.593386622}
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