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Simplifying 2z2 + -7z + -35 = 0 Reorder the terms: -35 + -7z + 2z2 = 0 Solving -35 + -7z + 2z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -3.5z + z2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -3.5z + 17.5 + z2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -3.5z + z2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -3.5z + z2 = 0 + 17.5 -3.5z + z2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -3.5z + z2 = 17.5 The z term is -3.5z. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5z + 3.0625 + z2 = 17.5 + 3.0625 Reorder the terms: 3.0625 + -3.5z + z2 = 17.5 + 3.0625 Combine like terms: 17.5 + 3.0625 = 20.5625 3.0625 + -3.5z + z2 = 20.5625 Factor a perfect square on the left side: (z + -1.75)(z + -1.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (z + -1.75) equal to 4.534589287 and -4.534589287.Subproblem 1
z + -1.75 = 4.534589287 Simplifying z + -1.75 = 4.534589287 Reorder the terms: -1.75 + z = 4.534589287 Solving -1.75 + z = 4.534589287 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + z = 4.534589287 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + z = 4.534589287 + 1.75 z = 4.534589287 + 1.75 Combine like terms: 4.534589287 + 1.75 = 6.284589287 z = 6.284589287 Simplifying z = 6.284589287Subproblem 2
z + -1.75 = -4.534589287 Simplifying z + -1.75 = -4.534589287 Reorder the terms: -1.75 + z = -4.534589287 Solving -1.75 + z = -4.534589287 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + z = -4.534589287 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + z = -4.534589287 + 1.75 z = -4.534589287 + 1.75 Combine like terms: -4.534589287 + 1.75 = -2.784589287 z = -2.784589287 Simplifying z = -2.784589287Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.284589287, -2.784589287}
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