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Simplifying 25z2 + -150z + 223 = 0 Reorder the terms: 223 + -150z + 25z2 = 0 Solving 223 + -150z + 25z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 8.92 + -6z + z2 = 0 Move the constant term to the right: Add '-8.92' to each side of the equation. 8.92 + -6z + -8.92 + z2 = 0 + -8.92 Reorder the terms: 8.92 + -8.92 + -6z + z2 = 0 + -8.92 Combine like terms: 8.92 + -8.92 = 0.00 0.00 + -6z + z2 = 0 + -8.92 -6z + z2 = 0 + -8.92 Combine like terms: 0 + -8.92 = -8.92 -6z + z2 = -8.92 The z term is -6z. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6z + 9 + z2 = -8.92 + 9 Reorder the terms: 9 + -6z + z2 = -8.92 + 9 Combine like terms: -8.92 + 9 = 0.08 9 + -6z + z2 = 0.08 Factor a perfect square on the left side: (z + -3)(z + -3) = 0.08 Calculate the square root of the right side: 0.282842712 Break this problem into two subproblems by setting (z + -3) equal to 0.282842712 and -0.282842712.Subproblem 1
z + -3 = 0.282842712 Simplifying z + -3 = 0.282842712 Reorder the terms: -3 + z = 0.282842712 Solving -3 + z = 0.282842712 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = 0.282842712 + 3 Combine like terms: -3 + 3 = 0 0 + z = 0.282842712 + 3 z = 0.282842712 + 3 Combine like terms: 0.282842712 + 3 = 3.282842712 z = 3.282842712 Simplifying z = 3.282842712Subproblem 2
z + -3 = -0.282842712 Simplifying z + -3 = -0.282842712 Reorder the terms: -3 + z = -0.282842712 Solving -3 + z = -0.282842712 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = -0.282842712 + 3 Combine like terms: -3 + 3 = 0 0 + z = -0.282842712 + 3 z = -0.282842712 + 3 Combine like terms: -0.282842712 + 3 = 2.717157288 z = 2.717157288 Simplifying z = 2.717157288Solution
The solution to the problem is based on the solutions from the subproblems. z = {3.282842712, 2.717157288}
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