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Simplifying 2x2 + 45x + 54 = 0 Reorder the terms: 54 + 45x + 2x2 = 0 Solving 54 + 45x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 27 + 22.5x + x2 = 0 Move the constant term to the right: Add '-27' to each side of the equation. 27 + 22.5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 22.5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 22.5x + x2 = 0 + -27 22.5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 22.5x + x2 = -27 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = -27 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = -27 + 126.5625 Combine like terms: -27 + 126.5625 = 99.5625 126.5625 + 22.5x + x2 = 99.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 99.5625 Calculate the square root of the right side: 9.978101022 Break this problem into two subproblems by setting (x + 11.25) equal to 9.978101022 and -9.978101022.Subproblem 1
x + 11.25 = 9.978101022 Simplifying x + 11.25 = 9.978101022 Reorder the terms: 11.25 + x = 9.978101022 Solving 11.25 + x = 9.978101022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 9.978101022 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 9.978101022 + -11.25 x = 9.978101022 + -11.25 Combine like terms: 9.978101022 + -11.25 = -1.271898978 x = -1.271898978 Simplifying x = -1.271898978Subproblem 2
x + 11.25 = -9.978101022 Simplifying x + 11.25 = -9.978101022 Reorder the terms: 11.25 + x = -9.978101022 Solving 11.25 + x = -9.978101022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -9.978101022 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -9.978101022 + -11.25 x = -9.978101022 + -11.25 Combine like terms: -9.978101022 + -11.25 = -21.228101022 x = -21.228101022 Simplifying x = -21.228101022Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.271898978, -21.228101022}
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