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Simplifying 4z2 + -56z + 19 = 0 Reorder the terms: 19 + -56z + 4z2 = 0 Solving 19 + -56z + 4z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.75 + -14z + z2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + -14z + -4.75 + z2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + -14z + z2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + -14z + z2 = 0 + -4.75 -14z + z2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 -14z + z2 = -4.75 The z term is -14z. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14z + 49 + z2 = -4.75 + 49 Reorder the terms: 49 + -14z + z2 = -4.75 + 49 Combine like terms: -4.75 + 49 = 44.25 49 + -14z + z2 = 44.25 Factor a perfect square on the left side: (z + -7)(z + -7) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (z + -7) equal to 6.652067348 and -6.652067348.Subproblem 1
z + -7 = 6.652067348 Simplifying z + -7 = 6.652067348 Reorder the terms: -7 + z = 6.652067348 Solving -7 + z = 6.652067348 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = 6.652067348 + 7 Combine like terms: -7 + 7 = 0 0 + z = 6.652067348 + 7 z = 6.652067348 + 7 Combine like terms: 6.652067348 + 7 = 13.652067348 z = 13.652067348 Simplifying z = 13.652067348Subproblem 2
z + -7 = -6.652067348 Simplifying z + -7 = -6.652067348 Reorder the terms: -7 + z = -6.652067348 Solving -7 + z = -6.652067348 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = -6.652067348 + 7 Combine like terms: -7 + 7 = 0 0 + z = -6.652067348 + 7 z = -6.652067348 + 7 Combine like terms: -6.652067348 + 7 = 0.347932652 z = 0.347932652 Simplifying z = 0.347932652Solution
The solution to the problem is based on the solutions from the subproblems. z = {13.652067348, 0.347932652}
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