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Simplifying 4.9x2 + 330x + -1320 = 0 Reorder the terms: -1320 + 330x + 4.9x2 = 0 Solving -1320 + 330x + 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'. -269.3877551 + 67.34693878x + x2 = 0 Move the constant term to the right: Add '269.3877551' to each side of the equation. -269.3877551 + 67.34693878x + 269.3877551 + x2 = 0 + 269.3877551 Reorder the terms: -269.3877551 + 269.3877551 + 67.34693878x + x2 = 0 + 269.3877551 Combine like terms: -269.3877551 + 269.3877551 = 0.0000000 0.0000000 + 67.34693878x + x2 = 0 + 269.3877551 67.34693878x + x2 = 0 + 269.3877551 Combine like terms: 0 + 269.3877551 = 269.3877551 67.34693878x + x2 = 269.3877551 The x term is 67.34693878x. Take half its coefficient (33.67346939). Square it (1133.902541) and add it to both sides. Add '1133.902541' to each side of the equation. 67.34693878x + 1133.902541 + x2 = 269.3877551 + 1133.902541 Reorder the terms: 1133.902541 + 67.34693878x + x2 = 269.3877551 + 1133.902541 Combine like terms: 269.3877551 + 1133.902541 = 1403.2902961 1133.902541 + 67.34693878x + x2 = 1403.2902961 Factor a perfect square on the left side: (x + 33.67346939)(x + 33.67346939) = 1403.2902961 Calculate the square root of the right side: 37.460516495 Break this problem into two subproblems by setting (x + 33.67346939) equal to 37.460516495 and -37.460516495.Subproblem 1
x + 33.67346939 = 37.460516495 Simplifying x + 33.67346939 = 37.460516495 Reorder the terms: 33.67346939 + x = 37.460516495 Solving 33.67346939 + x = 37.460516495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.67346939' to each side of the equation. 33.67346939 + -33.67346939 + x = 37.460516495 + -33.67346939 Combine like terms: 33.67346939 + -33.67346939 = 0.00000000 0.00000000 + x = 37.460516495 + -33.67346939 x = 37.460516495 + -33.67346939 Combine like terms: 37.460516495 + -33.67346939 = 3.787047105 x = 3.787047105 Simplifying x = 3.787047105Subproblem 2
x + 33.67346939 = -37.460516495 Simplifying x + 33.67346939 = -37.460516495 Reorder the terms: 33.67346939 + x = -37.460516495 Solving 33.67346939 + x = -37.460516495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.67346939' to each side of the equation. 33.67346939 + -33.67346939 + x = -37.460516495 + -33.67346939 Combine like terms: 33.67346939 + -33.67346939 = 0.00000000 0.00000000 + x = -37.460516495 + -33.67346939 x = -37.460516495 + -33.67346939 Combine like terms: -37.460516495 + -33.67346939 = -71.133985885 x = -71.133985885 Simplifying x = -71.133985885Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.787047105, -71.133985885}
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