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Simplifying 0 = 9x2 + 99x + 244 Reorder the terms: 0 = 244 + 99x + 9x2 Solving 0 = 244 + 99x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -244 = -244 -244 + -99x + -9x2 = 244 + 99x + 9x2 + -244 + -99x + -9x2 Reorder the terms: -244 + -99x + -9x2 = 244 + -244 + 99x + -99x + 9x2 + -9x2 Combine like terms: 244 + -244 = 0 -244 + -99x + -9x2 = 0 + 99x + -99x + 9x2 + -9x2 -244 + -99x + -9x2 = 99x + -99x + 9x2 + -9x2 Combine like terms: 99x + -99x = 0 -244 + -99x + -9x2 = 0 + 9x2 + -9x2 -244 + -99x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -244 + -99x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(244 + 99x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(244 + 99x + 9x2)' equal to zero and attempt to solve: Simplifying 244 + 99x + 9x2 = 0 Solving 244 + 99x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 27.11111111 + 11x + x2 = 0 Move the constant term to the right: Add '-27.11111111' to each side of the equation. 27.11111111 + 11x + -27.11111111 + x2 = 0 + -27.11111111 Reorder the terms: 27.11111111 + -27.11111111 + 11x + x2 = 0 + -27.11111111 Combine like terms: 27.11111111 + -27.11111111 = 0.00000000 0.00000000 + 11x + x2 = 0 + -27.11111111 11x + x2 = 0 + -27.11111111 Combine like terms: 0 + -27.11111111 = -27.11111111 11x + x2 = -27.11111111 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -27.11111111 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -27.11111111 + 30.25 Combine like terms: -27.11111111 + 30.25 = 3.13888889 30.25 + 11x + x2 = 3.13888889 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 3.13888889 Calculate the square root of the right side: 1.771690969 Break this problem into two subproblems by setting (x + 5.5) equal to 1.771690969 and -1.771690969.Subproblem 1
x + 5.5 = 1.771690969 Simplifying x + 5.5 = 1.771690969 Reorder the terms: 5.5 + x = 1.771690969 Solving 5.5 + x = 1.771690969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 1.771690969 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 1.771690969 + -5.5 x = 1.771690969 + -5.5 Combine like terms: 1.771690969 + -5.5 = -3.728309031 x = -3.728309031 Simplifying x = -3.728309031Subproblem 2
x + 5.5 = -1.771690969 Simplifying x + 5.5 = -1.771690969 Reorder the terms: 5.5 + x = -1.771690969 Solving 5.5 + x = -1.771690969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -1.771690969 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -1.771690969 + -5.5 x = -1.771690969 + -5.5 Combine like terms: -1.771690969 + -5.5 = -7.271690969 x = -7.271690969 Simplifying x = -7.271690969Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.728309031, -7.271690969}Solution
x = {-3.728309031, -7.271690969}
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