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Simplifying 49x2 + -14x + -64 = 0 Reorder the terms: -64 + -14x + 49x2 = 0 Solving -64 + -14x + 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'. -1.306122449 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '1.306122449' to each side of the equation. -1.306122449 + -0.2857142857x + 1.306122449 + x2 = 0 + 1.306122449 Reorder the terms: -1.306122449 + 1.306122449 + -0.2857142857x + x2 = 0 + 1.306122449 Combine like terms: -1.306122449 + 1.306122449 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 1.306122449 -0.2857142857x + x2 = 0 + 1.306122449 Combine like terms: 0 + 1.306122449 = 1.306122449 -0.2857142857x + x2 = 1.306122449 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 1.306122449 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 1.306122449 + 0.02040816328 Combine like terms: 1.306122449 + 0.02040816328 = 1.32653061228 0.02040816328 + -0.2857142857x + x2 = 1.32653061228 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 1.32653061228 Calculate the square root of the right side: 1.151751107 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.151751107 and -1.151751107.Subproblem 1
x + -0.1428571429 = 1.151751107 Simplifying x + -0.1428571429 = 1.151751107 Reorder the terms: -0.1428571429 + x = 1.151751107 Solving -0.1428571429 + x = 1.151751107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 1.151751107 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.151751107 + 0.1428571429 x = 1.151751107 + 0.1428571429 Combine like terms: 1.151751107 + 0.1428571429 = 1.2946082499 x = 1.2946082499 Simplifying x = 1.2946082499Subproblem 2
x + -0.1428571429 = -1.151751107 Simplifying x + -0.1428571429 = -1.151751107 Reorder the terms: -0.1428571429 + x = -1.151751107 Solving -0.1428571429 + x = -1.151751107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -1.151751107 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.151751107 + 0.1428571429 x = -1.151751107 + 0.1428571429 Combine like terms: -1.151751107 + 0.1428571429 = -1.0088939641 x = -1.0088939641 Simplifying x = -1.0088939641Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2946082499, -1.0088939641}
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