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Simplifying 4.9x2 + -19x + 10 = 0 Reorder the terms: 10 + -19x + 4.9x2 = 0 Solving 10 + -19x + 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'. 2.040816327 + -3.87755102x + x2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + -3.87755102x + -2.040816327 + x2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + -3.87755102x + x2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + -3.87755102x + x2 = 0 + -2.040816327 -3.87755102x + x2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 -3.87755102x + x2 = -2.040816327 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 = -2.040816327 + 3.758850478 Reorder the terms: 3.758850478 + -3.87755102x + x2 = -2.040816327 + 3.758850478 Combine like terms: -2.040816327 + 3.758850478 = 1.718034151 3.758850478 + -3.87755102x + x2 = 1.718034151 Factor a perfect square on the left side: (x + -1.93877551)(x + -1.93877551) = 1.718034151 Calculate the square root of the right side: 1.310738018 Break this problem into two subproblems by setting (x + -1.93877551) equal to 1.310738018 and -1.310738018.Subproblem 1
x + -1.93877551 = 1.310738018 Simplifying x + -1.93877551 = 1.310738018 Reorder the terms: -1.93877551 + x = 1.310738018 Solving -1.93877551 + x = 1.310738018 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 = 1.310738018 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + x = 1.310738018 + 1.93877551 x = 1.310738018 + 1.93877551 Combine like terms: 1.310738018 + 1.93877551 = 3.249513528 x = 3.249513528 Simplifying x = 3.249513528Subproblem 2
x + -1.93877551 = -1.310738018 Simplifying x + -1.93877551 = -1.310738018 Reorder the terms: -1.93877551 + x = -1.310738018 Solving -1.93877551 + x = -1.310738018 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 = -1.310738018 + 1.93877551 Combine like terms: -1.93877551 + 1.93877551 = 0.00000000 0.00000000 + x = -1.310738018 + 1.93877551 x = -1.310738018 + 1.93877551 Combine like terms: -1.310738018 + 1.93877551 = 0.628037492 x = 0.628037492 Simplifying x = 0.628037492Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.249513528, 0.628037492}
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