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Simplifying 3.14x2 + x = 621 Reorder the terms: x + 3.14x2 = 621 Solving x + 3.14x2 = 621 Solving for variable 'x'. Reorder the terms: -621 + x + 3.14x2 = 621 + -621 Combine like terms: 621 + -621 = 0 -621 + x + 3.14x2 = 0 Begin completing the square. Divide all terms by 3.14 the coefficient of the squared term: Divide each side by '3.14'. -197.7707006 + 0.3184713376x + x2 = 0 Move the constant term to the right: Add '197.7707006' to each side of the equation. -197.7707006 + 0.3184713376x + 197.7707006 + x2 = 0 + 197.7707006 Reorder the terms: -197.7707006 + 197.7707006 + 0.3184713376x + x2 = 0 + 197.7707006 Combine like terms: -197.7707006 + 197.7707006 = 0.0000000 0.0000000 + 0.3184713376x + x2 = 0 + 197.7707006 0.3184713376x + x2 = 0 + 197.7707006 Combine like terms: 0 + 197.7707006 = 197.7707006 0.3184713376x + x2 = 197.7707006 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3184713376x + 0.25 + x2 = 197.7707006 + 0.25 Reorder the terms: 0.25 + 0.3184713376x + x2 = 197.7707006 + 0.25 Combine like terms: 197.7707006 + 0.25 = 198.0207006 0.25 + 0.3184713376x + x2 = 198.0207006 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 198.0207006 Calculate the square root of the right side: 14.071982824 Break this problem into two subproblems by setting (x + 0.5) equal to 14.071982824 and -14.071982824.Subproblem 1
x + 0.5 = 14.071982824 Simplifying x + 0.5 = 14.071982824 Reorder the terms: 0.5 + x = 14.071982824 Solving 0.5 + x = 14.071982824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 14.071982824 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.071982824 + -0.5 x = 14.071982824 + -0.5 Combine like terms: 14.071982824 + -0.5 = 13.571982824 x = 13.571982824 Simplifying x = 13.571982824Subproblem 2
x + 0.5 = -14.071982824 Simplifying x + 0.5 = -14.071982824 Reorder the terms: 0.5 + x = -14.071982824 Solving 0.5 + x = -14.071982824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -14.071982824 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.071982824 + -0.5 x = -14.071982824 + -0.5 Combine like terms: -14.071982824 + -0.5 = -14.571982824 x = -14.571982824 Simplifying x = -14.571982824Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.571982824, -14.571982824}
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