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Simplifying 7z + -9z2 = -4 Solving 7z + -9z2 = -4 Solving for variable 'z'. Reorder the terms: 4 + 7z + -9z2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 7z + -9z2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.4444444444 + -0.7777777778z + z2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.7777777778z + 0.4444444444 + z2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.7777777778z + z2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.7777777778z + z2 = 0 + 0.4444444444 -0.7777777778z + z2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.7777777778z + z2 = 0.4444444444 The z term is -0.7777777778z. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778z + 0.1512345679 + z2 = 0.4444444444 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778z + z2 = 0.4444444444 + 0.1512345679 Combine like terms: 0.4444444444 + 0.1512345679 = 0.5956790123 0.1512345679 + -0.7777777778z + z2 = 0.5956790123 Factor a perfect square on the left side: (z + -0.3888888889)(z + -0.3888888889) = 0.5956790123 Calculate the square root of the right side: 0.771802444 Break this problem into two subproblems by setting (z + -0.3888888889) equal to 0.771802444 and -0.771802444.Subproblem 1
z + -0.3888888889 = 0.771802444 Simplifying z + -0.3888888889 = 0.771802444 Reorder the terms: -0.3888888889 + z = 0.771802444 Solving -0.3888888889 + z = 0.771802444 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + z = 0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + z = 0.771802444 + 0.3888888889 z = 0.771802444 + 0.3888888889 Combine like terms: 0.771802444 + 0.3888888889 = 1.1606913329 z = 1.1606913329 Simplifying z = 1.1606913329Subproblem 2
z + -0.3888888889 = -0.771802444 Simplifying z + -0.3888888889 = -0.771802444 Reorder the terms: -0.3888888889 + z = -0.771802444 Solving -0.3888888889 + z = -0.771802444 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + z = -0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + z = -0.771802444 + 0.3888888889 z = -0.771802444 + 0.3888888889 Combine like terms: -0.771802444 + 0.3888888889 = -0.3829135551 z = -0.3829135551 Simplifying z = -0.3829135551Solution
The solution to the problem is based on the solutions from the subproblems. z = {1.1606913329, -0.3829135551}
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