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Simplifying 0 = 2.49(20 + -1x)(1 + -1x) + -1x2 Multiply (20 + -1x) * (1 + -1x) 0 = 2.49(20(1 + -1x) + -1x * (1 + -1x)) + -1x2 0 = 2.49((1 * 20 + -1x * 20) + -1x * (1 + -1x)) + -1x2 0 = 2.49((20 + -20x) + -1x * (1 + -1x)) + -1x2 0 = 2.49(20 + -20x + (1 * -1x + -1x * -1x)) + -1x2 0 = 2.49(20 + -20x + (-1x + 1x2)) + -1x2 Combine like terms: -20x + -1x = -21x 0 = 2.49(20 + -21x + 1x2) + -1x2 0 = (20 * 2.49 + -21x * 2.49 + 1x2 * 2.49) + -1x2 0 = (49.8 + -52.29x + 2.49x2) + -1x2 Combine like terms: 2.49x2 + -1x2 = 1.49x2 0 = 49.8 + -52.29x + 1.49x2 Solving 0 = 49.8 + -52.29x + 1.49x2 Solving for variable 'x'. Combine like terms: 0 + -49.8 = -49.8 -49.8 + 52.29x + -1.49x2 = 49.8 + -52.29x + 1.49x2 + -49.8 + 52.29x + -1.49x2 Reorder the terms: -49.8 + 52.29x + -1.49x2 = 49.8 + -49.8 + -52.29x + 52.29x + 1.49x2 + -1.49x2 Combine like terms: 49.8 + -49.8 = 0.0 -49.8 + 52.29x + -1.49x2 = 0.0 + -52.29x + 52.29x + 1.49x2 + -1.49x2 -49.8 + 52.29x + -1.49x2 = -52.29x + 52.29x + 1.49x2 + -1.49x2 Combine like terms: -52.29x + 52.29x = 0.00 -49.8 + 52.29x + -1.49x2 = 0.00 + 1.49x2 + -1.49x2 -49.8 + 52.29x + -1.49x2 = 1.49x2 + -1.49x2 Combine like terms: 1.49x2 + -1.49x2 = 0.00 -49.8 + 52.29x + -1.49x2 = 0.00 Begin completing the square. Divide all terms by -1.49 the coefficient of the squared term: Divide each side by '-1.49'. 33.42281879 + -35.09395973x + x2 = 0 Move the constant term to the right: Add '-33.42281879' to each side of the equation. 33.42281879 + -35.09395973x + -33.42281879 + x2 = 0 + -33.42281879 Reorder the terms: 33.42281879 + -33.42281879 + -35.09395973x + x2 = 0 + -33.42281879 Combine like terms: 33.42281879 + -33.42281879 = 0.00000000 0.00000000 + -35.09395973x + x2 = 0 + -33.42281879 -35.09395973x + x2 = 0 + -33.42281879 Combine like terms: 0 + -33.42281879 = -33.42281879 -35.09395973x + x2 = -33.42281879 The x term is -35.09395973x. Take half its coefficient (-17.54697987). Square it (307.8965026) and add it to both sides. Add '307.8965026' to each side of the equation. -35.09395973x + 307.8965026 + x2 = -33.42281879 + 307.8965026 Reorder the terms: 307.8965026 + -35.09395973x + x2 = -33.42281879 + 307.8965026 Combine like terms: -33.42281879 + 307.8965026 = 274.47368381 307.8965026 + -35.09395973x + x2 = 274.47368381 Factor a perfect square on the left side: (x + -17.54697987)(x + -17.54697987) = 274.47368381 Calculate the square root of the right side: 16.567247321 Break this problem into two subproblems by setting (x + -17.54697987) equal to 16.567247321 and -16.567247321.Subproblem 1
x + -17.54697987 = 16.567247321 Simplifying x + -17.54697987 = 16.567247321 Reorder the terms: -17.54697987 + x = 16.567247321 Solving -17.54697987 + x = 16.567247321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.54697987' to each side of the equation. -17.54697987 + 17.54697987 + x = 16.567247321 + 17.54697987 Combine like terms: -17.54697987 + 17.54697987 = 0.00000000 0.00000000 + x = 16.567247321 + 17.54697987 x = 16.567247321 + 17.54697987 Combine like terms: 16.567247321 + 17.54697987 = 34.114227191 x = 34.114227191 Simplifying x = 34.114227191Subproblem 2
x + -17.54697987 = -16.567247321 Simplifying x + -17.54697987 = -16.567247321 Reorder the terms: -17.54697987 + x = -16.567247321 Solving -17.54697987 + x = -16.567247321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.54697987' to each side of the equation. -17.54697987 + 17.54697987 + x = -16.567247321 + 17.54697987 Combine like terms: -17.54697987 + 17.54697987 = 0.00000000 0.00000000 + x = -16.567247321 + 17.54697987 x = -16.567247321 + 17.54697987 Combine like terms: -16.567247321 + 17.54697987 = 0.979732549 x = 0.979732549 Simplifying x = 0.979732549Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.114227191, 0.979732549}
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