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Simplifying 45.9 + 4.9x2 + -30x = 0 Reorder the terms: 45.9 + -30x + 4.9x2 = 0 Solving 45.9 + -30x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 9.367346939 + -6.12244898x + x2 = 0 Move the constant term to the right: Add '-9.367346939' to each side of the equation. 9.367346939 + -6.12244898x + -9.367346939 + x2 = 0 + -9.367346939 Reorder the terms: 9.367346939 + -9.367346939 + -6.12244898x + x2 = 0 + -9.367346939 Combine like terms: 9.367346939 + -9.367346939 = 0.000000000 0.000000000 + -6.12244898x + x2 = 0 + -9.367346939 -6.12244898x + x2 = 0 + -9.367346939 Combine like terms: 0 + -9.367346939 = -9.367346939 -6.12244898x + x2 = -9.367346939 The x term is -6.12244898x. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898x + 9.371095378 + x2 = -9.367346939 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898x + x2 = -9.367346939 + 9.371095378 Combine like terms: -9.367346939 + 9.371095378 = 0.003748439 9.371095378 + -6.12244898x + x2 = 0.003748439 Factor a perfect square on the left side: (x + -3.06122449)(x + -3.06122449) = 0.003748439 Calculate the square root of the right side: 0.061224497 Break this problem into two subproblems by setting (x + -3.06122449) equal to 0.061224497 and -0.061224497.Subproblem 1
x + -3.06122449 = 0.061224497 Simplifying x + -3.06122449 = 0.061224497 Reorder the terms: -3.06122449 + x = 0.061224497 Solving -3.06122449 + x = 0.061224497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = 0.061224497 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = 0.061224497 + 3.06122449 x = 0.061224497 + 3.06122449 Combine like terms: 0.061224497 + 3.06122449 = 3.122448987 x = 3.122448987 Simplifying x = 3.122448987Subproblem 2
x + -3.06122449 = -0.061224497 Simplifying x + -3.06122449 = -0.061224497 Reorder the terms: -3.06122449 + x = -0.061224497 Solving -3.06122449 + x = -0.061224497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = -0.061224497 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = -0.061224497 + 3.06122449 x = -0.061224497 + 3.06122449 Combine like terms: -0.061224497 + 3.06122449 = 2.999999993 x = 2.999999993 Simplifying x = 2.999999993Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.122448987, 2.999999993}
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