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Simplifying 0 = 44x2 + -48x + -9 Reorder the terms: 0 = -9 + -48x + 44x2 Solving 0 = -9 + -48x + 44x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + 48x + -44x2 = -9 + -48x + 44x2 + 9 + 48x + -44x2 Reorder the terms: 9 + 48x + -44x2 = -9 + 9 + -48x + 48x + 44x2 + -44x2 Combine like terms: -9 + 9 = 0 9 + 48x + -44x2 = 0 + -48x + 48x + 44x2 + -44x2 9 + 48x + -44x2 = -48x + 48x + 44x2 + -44x2 Combine like terms: -48x + 48x = 0 9 + 48x + -44x2 = 0 + 44x2 + -44x2 9 + 48x + -44x2 = 44x2 + -44x2 Combine like terms: 44x2 + -44x2 = 0 9 + 48x + -44x2 = 0 Begin completing the square. Divide all terms by -44 the coefficient of the squared term: Divide each side by '-44'. -0.2045454545 + -1.090909091x + x2 = 0 Move the constant term to the right: Add '0.2045454545' to each side of the equation. -0.2045454545 + -1.090909091x + 0.2045454545 + x2 = 0 + 0.2045454545 Reorder the terms: -0.2045454545 + 0.2045454545 + -1.090909091x + x2 = 0 + 0.2045454545 Combine like terms: -0.2045454545 + 0.2045454545 = 0.0000000000 0.0000000000 + -1.090909091x + x2 = 0 + 0.2045454545 -1.090909091x + x2 = 0 + 0.2045454545 Combine like terms: 0 + 0.2045454545 = 0.2045454545 -1.090909091x + x2 = 0.2045454545 The x term is -1.090909091x. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091x + 0.2975206612 + x2 = 0.2045454545 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091x + x2 = 0.2045454545 + 0.2975206612 Combine like terms: 0.2045454545 + 0.2975206612 = 0.5020661157 0.2975206612 + -1.090909091x + x2 = 0.5020661157 Factor a perfect square on the left side: (x + -0.5454545455)(x + -0.5454545455) = 0.5020661157 Calculate the square root of the right side: 0.708566239 Break this problem into two subproblems by setting (x + -0.5454545455) equal to 0.708566239 and -0.708566239.Subproblem 1
x + -0.5454545455 = 0.708566239 Simplifying x + -0.5454545455 = 0.708566239 Reorder the terms: -0.5454545455 + x = 0.708566239 Solving -0.5454545455 + x = 0.708566239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = 0.708566239 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = 0.708566239 + 0.5454545455 x = 0.708566239 + 0.5454545455 Combine like terms: 0.708566239 + 0.5454545455 = 1.2540207845 x = 1.2540207845 Simplifying x = 1.2540207845Subproblem 2
x + -0.5454545455 = -0.708566239 Simplifying x + -0.5454545455 = -0.708566239 Reorder the terms: -0.5454545455 + x = -0.708566239 Solving -0.5454545455 + x = -0.708566239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = -0.708566239 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = -0.708566239 + 0.5454545455 x = -0.708566239 + 0.5454545455 Combine like terms: -0.708566239 + 0.5454545455 = -0.1631116935 x = -0.1631116935 Simplifying x = -0.1631116935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2540207845, -0.1631116935}
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