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Simplifying 45x2 + -492x + -2360 = 0 Reorder the terms: -2360 + -492x + 45x2 = 0 Solving -2360 + -492x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -52.44444444 + -10.93333333x + x2 = 0 Move the constant term to the right: Add '52.44444444' to each side of the equation. -52.44444444 + -10.93333333x + 52.44444444 + x2 = 0 + 52.44444444 Reorder the terms: -52.44444444 + 52.44444444 + -10.93333333x + x2 = 0 + 52.44444444 Combine like terms: -52.44444444 + 52.44444444 = 0.00000000 0.00000000 + -10.93333333x + x2 = 0 + 52.44444444 -10.93333333x + x2 = 0 + 52.44444444 Combine like terms: 0 + 52.44444444 = 52.44444444 -10.93333333x + x2 = 52.44444444 The x term is -10.93333333x. Take half its coefficient (-5.466666665). Square it (29.88444443) and add it to both sides. Add '29.88444443' to each side of the equation. -10.93333333x + 29.88444443 + x2 = 52.44444444 + 29.88444443 Reorder the terms: 29.88444443 + -10.93333333x + x2 = 52.44444444 + 29.88444443 Combine like terms: 52.44444444 + 29.88444443 = 82.32888887 29.88444443 + -10.93333333x + x2 = 82.32888887 Factor a perfect square on the left side: (x + -5.466666665)(x + -5.466666665) = 82.32888887 Calculate the square root of the right side: 9.073526815 Break this problem into two subproblems by setting (x + -5.466666665) equal to 9.073526815 and -9.073526815.Subproblem 1
x + -5.466666665 = 9.073526815 Simplifying x + -5.466666665 = 9.073526815 Reorder the terms: -5.466666665 + x = 9.073526815 Solving -5.466666665 + x = 9.073526815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.466666665' to each side of the equation. -5.466666665 + 5.466666665 + x = 9.073526815 + 5.466666665 Combine like terms: -5.466666665 + 5.466666665 = 0.000000000 0.000000000 + x = 9.073526815 + 5.466666665 x = 9.073526815 + 5.466666665 Combine like terms: 9.073526815 + 5.466666665 = 14.54019348 x = 14.54019348 Simplifying x = 14.54019348Subproblem 2
x + -5.466666665 = -9.073526815 Simplifying x + -5.466666665 = -9.073526815 Reorder the terms: -5.466666665 + x = -9.073526815 Solving -5.466666665 + x = -9.073526815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.466666665' to each side of the equation. -5.466666665 + 5.466666665 + x = -9.073526815 + 5.466666665 Combine like terms: -5.466666665 + 5.466666665 = 0.000000000 0.000000000 + x = -9.073526815 + 5.466666665 x = -9.073526815 + 5.466666665 Combine like terms: -9.073526815 + 5.466666665 = -3.60686015 x = -3.60686015 Simplifying x = -3.60686015Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.54019348, -3.60686015}
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