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Simplifying 25z2 + -100z + 97 = 0 Reorder the terms: 97 + -100z + 25z2 = 0 Solving 97 + -100z + 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'. 3.88 + -4z + z2 = 0 Move the constant term to the right: Add '-3.88' to each side of the equation. 3.88 + -4z + -3.88 + z2 = 0 + -3.88 Reorder the terms: 3.88 + -3.88 + -4z + z2 = 0 + -3.88 Combine like terms: 3.88 + -3.88 = 0.00 0.00 + -4z + z2 = 0 + -3.88 -4z + z2 = 0 + -3.88 Combine like terms: 0 + -3.88 = -3.88 -4z + z2 = -3.88 The z term is -4z. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4z + 4 + z2 = -3.88 + 4 Reorder the terms: 4 + -4z + z2 = -3.88 + 4 Combine like terms: -3.88 + 4 = 0.12 4 + -4z + z2 = 0.12 Factor a perfect square on the left side: (z + -2)(z + -2) = 0.12 Calculate the square root of the right side: 0.346410162 Break this problem into two subproblems by setting (z + -2) equal to 0.346410162 and -0.346410162.Subproblem 1
z + -2 = 0.346410162 Simplifying z + -2 = 0.346410162 Reorder the terms: -2 + z = 0.346410162 Solving -2 + z = 0.346410162 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 0.346410162 + 2 Combine like terms: -2 + 2 = 0 0 + z = 0.346410162 + 2 z = 0.346410162 + 2 Combine like terms: 0.346410162 + 2 = 2.346410162 z = 2.346410162 Simplifying z = 2.346410162Subproblem 2
z + -2 = -0.346410162 Simplifying z + -2 = -0.346410162 Reorder the terms: -2 + z = -0.346410162 Solving -2 + z = -0.346410162 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = -0.346410162 + 2 Combine like terms: -2 + 2 = 0 0 + z = -0.346410162 + 2 z = -0.346410162 + 2 Combine like terms: -0.346410162 + 2 = 1.653589838 z = 1.653589838 Simplifying z = 1.653589838Solution
The solution to the problem is based on the solutions from the subproblems. z = {2.346410162, 1.653589838}
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