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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 = 6.003748437 3.758850478 + 3.87755102x + x2 = 6.003748437 Factor a perfect square on the left side: (x + 1.93877551)(x + 1.93877551) = 6.003748437 Calculate the square root of the right side: 2.45025477 Break this problem into two subproblems by setting (x + 1.93877551) equal to 2.45025477 and -2.45025477.Subproblem 1
x + 1.93877551 = 2.45025477 Simplifying x + 1.93877551 = 2.45025477 Reorder the terms: 1.93877551 + x = 2.45025477 Solving 1.93877551 + x = 2.45025477 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 = 2.45025477 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + x = 2.45025477 + -1.93877551 x = 2.45025477 + -1.93877551 Combine like terms: 2.45025477 + -1.93877551 = 0.51147926 x = 0.51147926 Simplifying x = 0.51147926Subproblem 2
x + 1.93877551 = -2.45025477 Simplifying x + 1.93877551 = -2.45025477 Reorder the terms: 1.93877551 + x = -2.45025477 Solving 1.93877551 + x = -2.45025477 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 = -2.45025477 + -1.93877551 Combine like terms: 1.93877551 + -1.93877551 = 0.00000000 0.00000000 + x = -2.45025477 + -1.93877551 x = -2.45025477 + -1.93877551 Combine like terms: -2.45025477 + -1.93877551 = -4.38903028 x = -4.38903028 Simplifying x = -4.38903028Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.51147926, -4.38903028}
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