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Simplifying 0.29z2 + -180 = 0.630z Reorder the terms: -180 + 0.29z2 = 0.630z Solving -180 + 0.29z2 = 0.630z Solving for variable 'z'. Reorder the terms: -180 + -0.630z + 0.29z2 = 0.630z + -0.630z Combine like terms: 0.630z + -0.630z = 0.000 -180 + -0.630z + 0.29z2 = 0.000 Begin completing the square. Divide all terms by 0.29 the coefficient of the squared term: Divide each side by '0.29'. -620.6896552 + -2.172413793z + z2 = 0.0 Move the constant term to the right: Add '620.6896552' to each side of the equation. -620.6896552 + -2.172413793z + 620.6896552 + z2 = 0.0 + 620.6896552 Reorder the terms: -620.6896552 + 620.6896552 + -2.172413793z + z2 = 0.0 + 620.6896552 Combine like terms: -620.6896552 + 620.6896552 = 0.0000000 0.0000000 + -2.172413793z + z2 = 0.0 + 620.6896552 -2.172413793z + z2 = 0.0 + 620.6896552 Combine like terms: 0.0 + 620.6896552 = 620.6896552 -2.172413793z + z2 = 620.6896552 The z term is -2.172413793z. Take half its coefficient (-1.086206897). Square it (1.179845423) and add it to both sides. Add '1.179845423' to each side of the equation. -2.172413793z + 1.179845423 + z2 = 620.6896552 + 1.179845423 Reorder the terms: 1.179845423 + -2.172413793z + z2 = 620.6896552 + 1.179845423 Combine like terms: 620.6896552 + 1.179845423 = 621.869500623 1.179845423 + -2.172413793z + z2 = 621.869500623 Factor a perfect square on the left side: (z + -1.086206897)(z + -1.086206897) = 621.869500623 Calculate the square root of the right side: 24.937311415 Break this problem into two subproblems by setting (z + -1.086206897) equal to 24.937311415 and -24.937311415.Subproblem 1
z + -1.086206897 = 24.937311415 Simplifying z + -1.086206897 = 24.937311415 Reorder the terms: -1.086206897 + z = 24.937311415 Solving -1.086206897 + z = 24.937311415 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.086206897' to each side of the equation. -1.086206897 + 1.086206897 + z = 24.937311415 + 1.086206897 Combine like terms: -1.086206897 + 1.086206897 = 0.000000000 0.000000000 + z = 24.937311415 + 1.086206897 z = 24.937311415 + 1.086206897 Combine like terms: 24.937311415 + 1.086206897 = 26.023518312 z = 26.023518312 Simplifying z = 26.023518312Subproblem 2
z + -1.086206897 = -24.937311415 Simplifying z + -1.086206897 = -24.937311415 Reorder the terms: -1.086206897 + z = -24.937311415 Solving -1.086206897 + z = -24.937311415 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.086206897' to each side of the equation. -1.086206897 + 1.086206897 + z = -24.937311415 + 1.086206897 Combine like terms: -1.086206897 + 1.086206897 = 0.000000000 0.000000000 + z = -24.937311415 + 1.086206897 z = -24.937311415 + 1.086206897 Combine like terms: -24.937311415 + 1.086206897 = -23.851104518 z = -23.851104518 Simplifying z = -23.851104518Solution
The solution to the problem is based on the solutions from the subproblems. z = {26.023518312, -23.851104518}
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