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Simplifying -0.288x2 + 97.739x + -3264.869 = 0 Reorder the terms: -3264.869 + 97.739x + -0.288x2 = 0 Solving -3264.869 + 97.739x + -0.288x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.288 the coefficient of the squared term: Divide each side by '-0.288'. 11336.35069 + -339.3715278x + x2 = 0 Move the constant term to the right: Add '-11336.35069' to each side of the equation. 11336.35069 + -339.3715278x + -11336.35069 + x2 = 0 + -11336.35069 Reorder the terms: 11336.35069 + -11336.35069 + -339.3715278x + x2 = 0 + -11336.35069 Combine like terms: 11336.35069 + -11336.35069 = 0.00000 0.00000 + -339.3715278x + x2 = 0 + -11336.35069 -339.3715278x + x2 = 0 + -11336.35069 Combine like terms: 0 + -11336.35069 = -11336.35069 -339.3715278x + x2 = -11336.35069 The x term is -339.3715278x. Take half its coefficient (-169.6857639). Square it (28793.25847) and add it to both sides. Add '28793.25847' to each side of the equation. -339.3715278x + 28793.25847 + x2 = -11336.35069 + 28793.25847 Reorder the terms: 28793.25847 + -339.3715278x + x2 = -11336.35069 + 28793.25847 Combine like terms: -11336.35069 + 28793.25847 = 17456.90778 28793.25847 + -339.3715278x + x2 = 17456.90778 Factor a perfect square on the left side: (x + -169.6857639)(x + -169.6857639) = 17456.90778 Calculate the square root of the right side: 132.124591882 Break this problem into two subproblems by setting (x + -169.6857639) equal to 132.124591882 and -132.124591882.Subproblem 1
x + -169.6857639 = 132.124591882 Simplifying x + -169.6857639 = 132.124591882 Reorder the terms: -169.6857639 + x = 132.124591882 Solving -169.6857639 + x = 132.124591882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '169.6857639' to each side of the equation. -169.6857639 + 169.6857639 + x = 132.124591882 + 169.6857639 Combine like terms: -169.6857639 + 169.6857639 = 0.0000000 0.0000000 + x = 132.124591882 + 169.6857639 x = 132.124591882 + 169.6857639 Combine like terms: 132.124591882 + 169.6857639 = 301.810355782 x = 301.810355782 Simplifying x = 301.810355782Subproblem 2
x + -169.6857639 = -132.124591882 Simplifying x + -169.6857639 = -132.124591882 Reorder the terms: -169.6857639 + x = -132.124591882 Solving -169.6857639 + x = -132.124591882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '169.6857639' to each side of the equation. -169.6857639 + 169.6857639 + x = -132.124591882 + 169.6857639 Combine like terms: -169.6857639 + 169.6857639 = 0.0000000 0.0000000 + x = -132.124591882 + 169.6857639 x = -132.124591882 + 169.6857639 Combine like terms: -132.124591882 + 169.6857639 = 37.561172018 x = 37.561172018 Simplifying x = 37.561172018Solution
The solution to the problem is based on the solutions from the subproblems. x = {301.810355782, 37.561172018}
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