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Simplifying 49x2 + 14x = 1 Reorder the terms: 14x + 49x2 = 1 Solving 14x + 49x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 14x + 49x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 14x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.02040816327 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.02040816327' to each side of the equation. -0.02040816327 + 0.2857142857x + 0.02040816327 + x2 = 0 + 0.02040816327 Reorder the terms: -0.02040816327 + 0.02040816327 + 0.2857142857x + x2 = 0 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + 0.2857142857x + x2 = 0 + 0.02040816327 0.2857142857x + x2 = 0 + 0.02040816327 Combine like terms: 0 + 0.02040816327 = 0.02040816327 0.2857142857x + x2 = 0.02040816327 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 = 0.02040816327 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.02040816327 + 0.02040816328 Combine like terms: 0.02040816327 + 0.02040816328 = 0.04081632655 0.02040816328 + 0.2857142857x + x2 = 0.04081632655 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.04081632655 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.202030509 and -0.202030509.Subproblem 1
x + 0.1428571429 = 0.202030509 Simplifying x + 0.1428571429 = 0.202030509 Reorder the terms: 0.1428571429 + x = 0.202030509 Solving 0.1428571429 + x = 0.202030509 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 = 0.202030509 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.202030509 + -0.1428571429 x = 0.202030509 + -0.1428571429 Combine like terms: 0.202030509 + -0.1428571429 = 0.0591733661 x = 0.0591733661 Simplifying x = 0.0591733661Subproblem 2
x + 0.1428571429 = -0.202030509 Simplifying x + 0.1428571429 = -0.202030509 Reorder the terms: 0.1428571429 + x = -0.202030509 Solving 0.1428571429 + x = -0.202030509 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 = -0.202030509 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.202030509 + -0.1428571429 x = -0.202030509 + -0.1428571429 Combine like terms: -0.202030509 + -0.1428571429 = -0.3448876519 x = -0.3448876519 Simplifying x = -0.3448876519Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0591733661, -0.3448876519}
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