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Simplifying -4.9x2 + 19x = 11 Reorder the terms: 19x + -4.9x2 = 11 Solving 19x + -4.9x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 19x + -4.9x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 19x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 2.244897959 + -3.87755102x + x2 = 0 Move the constant term to the right: Add '-2.244897959' to each side of the equation. 2.244897959 + -3.87755102x + -2.244897959 + x2 = 0 + -2.244897959 Reorder the terms: 2.244897959 + -2.244897959 + -3.87755102x + x2 = 0 + -2.244897959 Combine like terms: 2.244897959 + -2.244897959 = 0.000000000 0.000000000 + -3.87755102x + x2 = 0 + -2.244897959 -3.87755102x + x2 = 0 + -2.244897959 Combine like terms: 0 + -2.244897959 = -2.244897959 -3.87755102x + x2 = -2.244897959 The x term is -3.87755102x. Take half its coefficient (-1.93877551). Square it (3.758850478) and add it to both sides. Add '3.758850478' to each side of the equation. -3.87755102x + 3.758850478 + x2 = -2.244897959 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102x + x2 = -2.244897959 + 3.758850478 Combine like terms: -2.244897959 + 3.758850478 = 1.513952519 3.758850478 + -3.87755102x + x2 = 1.513952519 Factor a perfect square on the left side: (x + -1.93877551)(x + -1.93877551) = 1.513952519 Calculate the square root of the right side: 1.230427779 Break this problem into two subproblems by setting (x + -1.93877551) equal to 1.230427779 and -1.230427779.Subproblem 1
x + -1.93877551 = 1.230427779 Simplifying x + -1.93877551 = 1.230427779 Reorder the terms: -1.93877551 + x = 1.230427779 Solving -1.93877551 + x = 1.230427779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.93877551' to each side of the equation. -1.93877551 + 1.93877551 + x = 1.230427779 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + x = 1.230427779 + 1.93877551 x = 1.230427779 + 1.93877551 Combine like terms: 1.230427779 + 1.93877551 = 3.169203289 x = 3.169203289 Simplifying x = 3.169203289Subproblem 2
x + -1.93877551 = -1.230427779 Simplifying x + -1.93877551 = -1.230427779 Reorder the terms: -1.93877551 + x = -1.230427779 Solving -1.93877551 + x = -1.230427779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.93877551' to each side of the equation. -1.93877551 + 1.93877551 + x = -1.230427779 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + x = -1.230427779 + 1.93877551 x = -1.230427779 + 1.93877551 Combine like terms: -1.230427779 + 1.93877551 = 0.708347731 x = 0.708347731 Simplifying x = 0.708347731Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.169203289, 0.708347731}
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