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Simplifying 14x2 + -475x + 308 = 0 Reorder the terms: 308 + -475x + 14x2 = 0 Solving 308 + -475x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 22 + -33.92857143x + x2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -33.92857143x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -33.92857143x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -33.92857143x + x2 = 0 + -22 -33.92857143x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -33.92857143x + x2 = -22 The x term is -33.92857143x. Take half its coefficient (-16.96428572). Square it (287.7869900) and add it to both sides. Add '287.7869900' to each side of the equation. -33.92857143x + 287.7869900 + x2 = -22 + 287.7869900 Reorder the terms: 287.7869900 + -33.92857143x + x2 = -22 + 287.7869900 Combine like terms: -22 + 287.7869900 = 265.78699 287.7869900 + -33.92857143x + x2 = 265.78699 Factor a perfect square on the left side: (x + -16.96428572)(x + -16.96428572) = 265.78699 Calculate the square root of the right side: 16.302974882 Break this problem into two subproblems by setting (x + -16.96428572) equal to 16.302974882 and -16.302974882.Subproblem 1
x + -16.96428572 = 16.302974882 Simplifying x + -16.96428572 = 16.302974882 Reorder the terms: -16.96428572 + x = 16.302974882 Solving -16.96428572 + x = 16.302974882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.96428572' to each side of the equation. -16.96428572 + 16.96428572 + x = 16.302974882 + 16.96428572 Combine like terms: -16.96428572 + 16.96428572 = 0.00000000 0.00000000 + x = 16.302974882 + 16.96428572 x = 16.302974882 + 16.96428572 Combine like terms: 16.302974882 + 16.96428572 = 33.267260602 x = 33.267260602 Simplifying x = 33.267260602Subproblem 2
x + -16.96428572 = -16.302974882 Simplifying x + -16.96428572 = -16.302974882 Reorder the terms: -16.96428572 + x = -16.302974882 Solving -16.96428572 + x = -16.302974882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.96428572' to each side of the equation. -16.96428572 + 16.96428572 + x = -16.302974882 + 16.96428572 Combine like terms: -16.96428572 + 16.96428572 = 0.00000000 0.00000000 + x = -16.302974882 + 16.96428572 x = -16.302974882 + 16.96428572 Combine like terms: -16.302974882 + 16.96428572 = 0.661310838 x = 0.661310838 Simplifying x = 0.661310838Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.267260602, 0.661310838}
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