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Simplifying 4.9x2 + 3x + -950 = 0 Reorder the terms: -950 + 3x + 4.9x2 = 0 Solving -950 + 3x + 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'. -193.877551 + 0.612244898x + x2 = 0 Move the constant term to the right: Add '193.877551' to each side of the equation. -193.877551 + 0.612244898x + 193.877551 + x2 = 0 + 193.877551 Reorder the terms: -193.877551 + 193.877551 + 0.612244898x + x2 = 0 + 193.877551 Combine like terms: -193.877551 + 193.877551 = 0.000000 0.000000 + 0.612244898x + x2 = 0 + 193.877551 0.612244898x + x2 = 0 + 193.877551 Combine like terms: 0 + 193.877551 = 193.877551 0.612244898x + x2 = 193.877551 The x term is 0.612244898x. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898x + 0.09371095378 + x2 = 193.877551 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898x + x2 = 193.877551 + 0.09371095378 Combine like terms: 193.877551 + 0.09371095378 = 193.97126195378 0.09371095378 + 0.612244898x + x2 = 193.97126195378 Factor a perfect square on the left side: (x + 0.306122449)(x + 0.306122449) = 193.97126195378 Calculate the square root of the right side: 13.927356603 Break this problem into two subproblems by setting (x + 0.306122449) equal to 13.927356603 and -13.927356603.Subproblem 1
x + 0.306122449 = 13.927356603 Simplifying x + 0.306122449 = 13.927356603 Reorder the terms: 0.306122449 + x = 13.927356603 Solving 0.306122449 + x = 13.927356603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = 13.927356603 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = 13.927356603 + -0.306122449 x = 13.927356603 + -0.306122449 Combine like terms: 13.927356603 + -0.306122449 = 13.621234154 x = 13.621234154 Simplifying x = 13.621234154Subproblem 2
x + 0.306122449 = -13.927356603 Simplifying x + 0.306122449 = -13.927356603 Reorder the terms: 0.306122449 + x = -13.927356603 Solving 0.306122449 + x = -13.927356603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = -13.927356603 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = -13.927356603 + -0.306122449 x = -13.927356603 + -0.306122449 Combine like terms: -13.927356603 + -0.306122449 = -14.233479052 x = -14.233479052 Simplifying x = -14.233479052Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.621234154, -14.233479052}
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