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Simplifying 5x2 + 6x2 + 6x = 123 Reorder the terms: 6x + 5x2 + 6x2 = 123 Combine like terms: 5x2 + 6x2 = 11x2 6x + 11x2 = 123 Solving 6x + 11x2 = 123 Solving for variable 'x'. Reorder the terms: -123 + 6x + 11x2 = 123 + -123 Combine like terms: 123 + -123 = 0 -123 + 6x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -11.18181818 + 0.5454545455x + x2 = 0 Move the constant term to the right: Add '11.18181818' to each side of the equation. -11.18181818 + 0.5454545455x + 11.18181818 + x2 = 0 + 11.18181818 Reorder the terms: -11.18181818 + 11.18181818 + 0.5454545455x + x2 = 0 + 11.18181818 Combine like terms: -11.18181818 + 11.18181818 = 0.00000000 0.00000000 + 0.5454545455x + x2 = 0 + 11.18181818 0.5454545455x + x2 = 0 + 11.18181818 Combine like terms: 0 + 11.18181818 = 11.18181818 0.5454545455x + x2 = 11.18181818 The x term is 0.5454545455x. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455x + 0.07438016533 + x2 = 11.18181818 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455x + x2 = 11.18181818 + 0.07438016533 Combine like terms: 11.18181818 + 0.07438016533 = 11.25619834533 0.07438016533 + 0.5454545455x + x2 = 11.25619834533 Factor a perfect square on the left side: (x + 0.2727272728)(x + 0.2727272728) = 11.25619834533 Calculate the square root of the right side: 3.355025834 Break this problem into two subproblems by setting (x + 0.2727272728) equal to 3.355025834 and -3.355025834.Subproblem 1
x + 0.2727272728 = 3.355025834 Simplifying x + 0.2727272728 = 3.355025834 Reorder the terms: 0.2727272728 + x = 3.355025834 Solving 0.2727272728 + x = 3.355025834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = 3.355025834 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = 3.355025834 + -0.2727272728 x = 3.355025834 + -0.2727272728 Combine like terms: 3.355025834 + -0.2727272728 = 3.0822985612 x = 3.0822985612 Simplifying x = 3.0822985612Subproblem 2
x + 0.2727272728 = -3.355025834 Simplifying x + 0.2727272728 = -3.355025834 Reorder the terms: 0.2727272728 + x = -3.355025834 Solving 0.2727272728 + x = -3.355025834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = -3.355025834 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = -3.355025834 + -0.2727272728 x = -3.355025834 + -0.2727272728 Combine like terms: -3.355025834 + -0.2727272728 = -3.6277531068 x = -3.6277531068 Simplifying x = -3.6277531068Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0822985612, -3.6277531068}
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