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Simplifying 7z * 5z + -2z + z = 33 Reorder the terms for easier multiplication: 7 * 5z * z + -2z + z = 33 Multiply 7 * 5 35z * z + -2z + z = 33 Multiply z * z 35z2 + -2z + z = 33 Reorder the terms: -2z + z + 35z2 = 33 Combine like terms: -2z + z = -1z -1z + 35z2 = 33 Solving -1z + 35z2 = 33 Solving for variable 'z'. Reorder the terms: -33 + -1z + 35z2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -1z + 35z2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.9428571429 + -0.02857142857z + z2 = 0 Move the constant term to the right: Add '0.9428571429' to each side of the equation. -0.9428571429 + -0.02857142857z + 0.9428571429 + z2 = 0 + 0.9428571429 Reorder the terms: -0.9428571429 + 0.9428571429 + -0.02857142857z + z2 = 0 + 0.9428571429 Combine like terms: -0.9428571429 + 0.9428571429 = 0.0000000000 0.0000000000 + -0.02857142857z + z2 = 0 + 0.9428571429 -0.02857142857z + z2 = 0 + 0.9428571429 Combine like terms: 0 + 0.9428571429 = 0.9428571429 -0.02857142857z + z2 = 0.9428571429 The z term is -0.02857142857z. Take half its coefficient (-0.01428571429). Square it (0.0002040816328) and add it to both sides. Add '0.0002040816328' to each side of the equation. -0.02857142857z + 0.0002040816328 + z2 = 0.9428571429 + 0.0002040816328 Reorder the terms: 0.0002040816328 + -0.02857142857z + z2 = 0.9428571429 + 0.0002040816328 Combine like terms: 0.9428571429 + 0.0002040816328 = 0.9430612245328 0.0002040816328 + -0.02857142857z + z2 = 0.9430612245328 Factor a perfect square on the left side: (z + -0.01428571429)(z + -0.01428571429) = 0.9430612245328 Calculate the square root of the right side: 0.971113394 Break this problem into two subproblems by setting (z + -0.01428571429) equal to 0.971113394 and -0.971113394.Subproblem 1
z + -0.01428571429 = 0.971113394 Simplifying z + -0.01428571429 = 0.971113394 Reorder the terms: -0.01428571429 + z = 0.971113394 Solving -0.01428571429 + z = 0.971113394 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.01428571429' to each side of the equation. -0.01428571429 + 0.01428571429 + z = 0.971113394 + 0.01428571429 Combine like terms: -0.01428571429 + 0.01428571429 = 0.00000000000 0.00000000000 + z = 0.971113394 + 0.01428571429 z = 0.971113394 + 0.01428571429 Combine like terms: 0.971113394 + 0.01428571429 = 0.98539910829 z = 0.98539910829 Simplifying z = 0.98539910829Subproblem 2
z + -0.01428571429 = -0.971113394 Simplifying z + -0.01428571429 = -0.971113394 Reorder the terms: -0.01428571429 + z = -0.971113394 Solving -0.01428571429 + z = -0.971113394 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.01428571429' to each side of the equation. -0.01428571429 + 0.01428571429 + z = -0.971113394 + 0.01428571429 Combine like terms: -0.01428571429 + 0.01428571429 = 0.00000000000 0.00000000000 + z = -0.971113394 + 0.01428571429 z = -0.971113394 + 0.01428571429 Combine like terms: -0.971113394 + 0.01428571429 = -0.95682767971 z = -0.95682767971 Simplifying z = -0.95682767971Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.98539910829, -0.95682767971}
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