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Simplifying 25z2 + -222 = 150z Reorder the terms: -222 + 25z2 = 150z Solving -222 + 25z2 = 150z Solving for variable 'z'. Reorder the terms: -222 + -150z + 25z2 = 150z + -150z Combine like terms: 150z + -150z = 0 -222 + -150z + 25z2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -8.88 + -6z + z2 = 0 Move the constant term to the right: Add '8.88' to each side of the equation. -8.88 + -6z + 8.88 + z2 = 0 + 8.88 Reorder the terms: -8.88 + 8.88 + -6z + z2 = 0 + 8.88 Combine like terms: -8.88 + 8.88 = 0.00 0.00 + -6z + z2 = 0 + 8.88 -6z + z2 = 0 + 8.88 Combine like terms: 0 + 8.88 = 8.88 -6z + z2 = 8.88 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 = 8.88 + 9 Reorder the terms: 9 + -6z + z2 = 8.88 + 9 Combine like terms: 8.88 + 9 = 17.88 9 + -6z + z2 = 17.88 Factor a perfect square on the left side: (z + -3)(z + -3) = 17.88 Calculate the square root of the right side: 4.228474902 Break this problem into two subproblems by setting (z + -3) equal to 4.228474902 and -4.228474902.Subproblem 1
z + -3 = 4.228474902 Simplifying z + -3 = 4.228474902 Reorder the terms: -3 + z = 4.228474902 Solving -3 + z = 4.228474902 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 = 4.228474902 + 3 Combine like terms: -3 + 3 = 0 0 + z = 4.228474902 + 3 z = 4.228474902 + 3 Combine like terms: 4.228474902 + 3 = 7.228474902 z = 7.228474902 Simplifying z = 7.228474902Subproblem 2
z + -3 = -4.228474902 Simplifying z + -3 = -4.228474902 Reorder the terms: -3 + z = -4.228474902 Solving -3 + z = -4.228474902 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 = -4.228474902 + 3 Combine like terms: -3 + 3 = 0 0 + z = -4.228474902 + 3 z = -4.228474902 + 3 Combine like terms: -4.228474902 + 3 = -1.228474902 z = -1.228474902 Simplifying z = -1.228474902Solution
The solution to the problem is based on the solutions from the subproblems. z = {7.228474902, -1.228474902}
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