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Simplifying 0 = 0.45x2 + 6x + -9075 Reorder the terms: 0 = -9075 + 6x + 0.45x2 Solving 0 = -9075 + 6x + 0.45x2 Solving for variable 'x'. Combine like terms: 0 + 9075 = 9075 9075 + -6x + -0.45x2 = -9075 + 6x + 0.45x2 + 9075 + -6x + -0.45x2 Reorder the terms: 9075 + -6x + -0.45x2 = -9075 + 9075 + 6x + -6x + 0.45x2 + -0.45x2 Combine like terms: -9075 + 9075 = 0 9075 + -6x + -0.45x2 = 0 + 6x + -6x + 0.45x2 + -0.45x2 9075 + -6x + -0.45x2 = 6x + -6x + 0.45x2 + -0.45x2 Combine like terms: 6x + -6x = 0 9075 + -6x + -0.45x2 = 0 + 0.45x2 + -0.45x2 9075 + -6x + -0.45x2 = 0.45x2 + -0.45x2 Combine like terms: 0.45x2 + -0.45x2 = 0.00 9075 + -6x + -0.45x2 = 0.00 Begin completing the square. Divide all terms by -0.45 the coefficient of the squared term: Divide each side by '-0.45'. -20166.66667 + 13.33333333x + x2 = 0 Move the constant term to the right: Add '20166.66667' to each side of the equation. -20166.66667 + 13.33333333x + 20166.66667 + x2 = 0 + 20166.66667 Reorder the terms: -20166.66667 + 20166.66667 + 13.33333333x + x2 = 0 + 20166.66667 Combine like terms: -20166.66667 + 20166.66667 = 0.00000 0.00000 + 13.33333333x + x2 = 0 + 20166.66667 13.33333333x + x2 = 0 + 20166.66667 Combine like terms: 0 + 20166.66667 = 20166.66667 13.33333333x + x2 = 20166.66667 The x term is 13.33333333x. Take half its coefficient (6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. 13.33333333x + 44.44444442 + x2 = 20166.66667 + 44.44444442 Reorder the terms: 44.44444442 + 13.33333333x + x2 = 20166.66667 + 44.44444442 Combine like terms: 20166.66667 + 44.44444442 = 20211.11111442 44.44444442 + 13.33333333x + x2 = 20211.11111442 Factor a perfect square on the left side: (x + 6.666666665)(x + 6.666666665) = 20211.11111442 Calculate the square root of the right side: 142.165787426 Break this problem into two subproblems by setting (x + 6.666666665) equal to 142.165787426 and -142.165787426.Subproblem 1
x + 6.666666665 = 142.165787426 Simplifying x + 6.666666665 = 142.165787426 Reorder the terms: 6.666666665 + x = 142.165787426 Solving 6.666666665 + x = 142.165787426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + x = 142.165787426 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = 142.165787426 + -6.666666665 x = 142.165787426 + -6.666666665 Combine like terms: 142.165787426 + -6.666666665 = 135.499120761 x = 135.499120761 Simplifying x = 135.499120761Subproblem 2
x + 6.666666665 = -142.165787426 Simplifying x + 6.666666665 = -142.165787426 Reorder the terms: 6.666666665 + x = -142.165787426 Solving 6.666666665 + x = -142.165787426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + x = -142.165787426 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + x = -142.165787426 + -6.666666665 x = -142.165787426 + -6.666666665 Combine like terms: -142.165787426 + -6.666666665 = -148.832454091 x = -148.832454091 Simplifying x = -148.832454091Solution
The solution to the problem is based on the solutions from the subproblems. x = {135.499120761, -148.832454091}
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