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Simplifying (7x + 1)(7x + 1) = 48 Reorder the terms: (1 + 7x)(7x + 1) = 48 Reorder the terms: (1 + 7x)(1 + 7x) = 48 Multiply (1 + 7x) * (1 + 7x) (1(1 + 7x) + 7x * (1 + 7x)) = 48 ((1 * 1 + 7x * 1) + 7x * (1 + 7x)) = 48 ((1 + 7x) + 7x * (1 + 7x)) = 48 (1 + 7x + (1 * 7x + 7x * 7x)) = 48 (1 + 7x + (7x + 49x2)) = 48 Combine like terms: 7x + 7x = 14x (1 + 14x + 49x2) = 48 Solving 1 + 14x + 49x2 = 48 Solving for variable 'x'. Reorder the terms: 1 + -48 + 14x + 49x2 = 48 + -48 Combine like terms: 1 + -48 = -47 -47 + 14x + 49x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -47 + 14x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.9591836735 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.9591836735' to each side of the equation. -0.9591836735 + 0.2857142857x + 0.9591836735 + x2 = 0 + 0.9591836735 Reorder the terms: -0.9591836735 + 0.9591836735 + 0.2857142857x + x2 = 0 + 0.9591836735 Combine like terms: -0.9591836735 + 0.9591836735 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.9591836735 0.2857142857x + x2 = 0 + 0.9591836735 Combine like terms: 0 + 0.9591836735 = 0.9591836735 0.2857142857x + x2 = 0.9591836735 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 = 0.9591836735 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.9591836735 + 0.02040816328 Combine like terms: 0.9591836735 + 0.02040816328 = 0.97959183678 0.02040816328 + 0.2857142857x + x2 = 0.97959183678 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.97959183678 Calculate the square root of the right side: 0.989743319 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.989743319 and -0.989743319.Subproblem 1
x + 0.1428571429 = 0.989743319 Simplifying x + 0.1428571429 = 0.989743319 Reorder the terms: 0.1428571429 + x = 0.989743319 Solving 0.1428571429 + x = 0.989743319 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 = 0.989743319 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.989743319 + -0.1428571429 x = 0.989743319 + -0.1428571429 Combine like terms: 0.989743319 + -0.1428571429 = 0.8468861761 x = 0.8468861761 Simplifying x = 0.8468861761Subproblem 2
x + 0.1428571429 = -0.989743319 Simplifying x + 0.1428571429 = -0.989743319 Reorder the terms: 0.1428571429 + x = -0.989743319 Solving 0.1428571429 + x = -0.989743319 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 = -0.989743319 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.989743319 + -0.1428571429 x = -0.989743319 + -0.1428571429 Combine like terms: -0.989743319 + -0.1428571429 = -1.1326004619 x = -1.1326004619 Simplifying x = -1.1326004619Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8468861761, -1.1326004619}
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