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Simplifying 49x2 + -31x + 4 = 0 Reorder the terms: 4 + -31x + 49x2 = 0 Solving 4 + -31x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.08163265306 + -0.6326530612x + x2 = 0 Move the constant term to the right: Add '-0.08163265306' to each side of the equation. 0.08163265306 + -0.6326530612x + -0.08163265306 + x2 = 0 + -0.08163265306 Reorder the terms: 0.08163265306 + -0.08163265306 + -0.6326530612x + x2 = 0 + -0.08163265306 Combine like terms: 0.08163265306 + -0.08163265306 = 0.00000000000 0.00000000000 + -0.6326530612x + x2 = 0 + -0.08163265306 -0.6326530612x + x2 = 0 + -0.08163265306 Combine like terms: 0 + -0.08163265306 = -0.08163265306 -0.6326530612x + x2 = -0.08163265306 The x term is -0.6326530612x. Take half its coefficient (-0.3163265306). Square it (0.1000624740) and add it to both sides. Add '0.1000624740' to each side of the equation. -0.6326530612x + 0.1000624740 + x2 = -0.08163265306 + 0.1000624740 Reorder the terms: 0.1000624740 + -0.6326530612x + x2 = -0.08163265306 + 0.1000624740 Combine like terms: -0.08163265306 + 0.1000624740 = 0.01842982094 0.1000624740 + -0.6326530612x + x2 = 0.01842982094 Factor a perfect square on the left side: (x + -0.3163265306)(x + -0.3163265306) = 0.01842982094 Calculate the square root of the right side: 0.135756477 Break this problem into two subproblems by setting (x + -0.3163265306) equal to 0.135756477 and -0.135756477.Subproblem 1
x + -0.3163265306 = 0.135756477 Simplifying x + -0.3163265306 = 0.135756477 Reorder the terms: -0.3163265306 + x = 0.135756477 Solving -0.3163265306 + x = 0.135756477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3163265306' to each side of the equation. -0.3163265306 + 0.3163265306 + x = 0.135756477 + 0.3163265306 Combine like terms: -0.3163265306 + 0.3163265306 = 0.0000000000 0.0000000000 + x = 0.135756477 + 0.3163265306 x = 0.135756477 + 0.3163265306 Combine like terms: 0.135756477 + 0.3163265306 = 0.4520830076 x = 0.4520830076 Simplifying x = 0.4520830076Subproblem 2
x + -0.3163265306 = -0.135756477 Simplifying x + -0.3163265306 = -0.135756477 Reorder the terms: -0.3163265306 + x = -0.135756477 Solving -0.3163265306 + x = -0.135756477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3163265306' to each side of the equation. -0.3163265306 + 0.3163265306 + x = -0.135756477 + 0.3163265306 Combine like terms: -0.3163265306 + 0.3163265306 = 0.0000000000 0.0000000000 + x = -0.135756477 + 0.3163265306 x = -0.135756477 + 0.3163265306 Combine like terms: -0.135756477 + 0.3163265306 = 0.1805700536 x = 0.1805700536 Simplifying x = 0.1805700536Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4520830076, 0.1805700536}
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