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Simplifying 49x2 + 14x + 1 = 3 Reorder the terms: 1 + 14x + 49x2 = 3 Solving 1 + 14x + 49x2 = 3 Solving for variable 'x'. Reorder the terms: 1 + -3 + 14x + 49x2 = 3 + -3 Combine like terms: 1 + -3 = -2 -2 + 14x + 49x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -2 + 14x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.04081632653 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.04081632653' to each side of the equation. -0.04081632653 + 0.2857142857x + 0.04081632653 + x2 = 0 + 0.04081632653 Reorder the terms: -0.04081632653 + 0.04081632653 + 0.2857142857x + x2 = 0 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + 0.2857142857x + x2 = 0 + 0.04081632653 0.2857142857x + x2 = 0 + 0.04081632653 Combine like terms: 0 + 0.04081632653 = 0.04081632653 0.2857142857x + x2 = 0.04081632653 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 = 0.04081632653 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.04081632653 + 0.02040816328 Combine like terms: 0.04081632653 + 0.02040816328 = 0.06122448981 0.02040816328 + 0.2857142857x + x2 = 0.06122448981 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.06122448981 Calculate the square root of the right side: 0.24743583 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.24743583 and -0.24743583.Subproblem 1
x + 0.1428571429 = 0.24743583 Simplifying x + 0.1428571429 = 0.24743583 Reorder the terms: 0.1428571429 + x = 0.24743583 Solving 0.1428571429 + x = 0.24743583 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 = 0.24743583 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.24743583 + -0.1428571429 x = 0.24743583 + -0.1428571429 Combine like terms: 0.24743583 + -0.1428571429 = 0.1045786871 x = 0.1045786871 Simplifying x = 0.1045786871Subproblem 2
x + 0.1428571429 = -0.24743583 Simplifying x + 0.1428571429 = -0.24743583 Reorder the terms: 0.1428571429 + x = -0.24743583 Solving 0.1428571429 + x = -0.24743583 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 = -0.24743583 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.24743583 + -0.1428571429 x = -0.24743583 + -0.1428571429 Combine like terms: -0.24743583 + -0.1428571429 = -0.3902929729 x = -0.3902929729 Simplifying x = -0.3902929729Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1045786871, -0.3902929729}
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