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Simplifying (4x + 7)(7x + 7) = 58x + 121 Reorder the terms: (7 + 4x)(7x + 7) = 58x + 121 Reorder the terms: (7 + 4x)(7 + 7x) = 58x + 121 Multiply (7 + 4x) * (7 + 7x) (7(7 + 7x) + 4x * (7 + 7x)) = 58x + 121 ((7 * 7 + 7x * 7) + 4x * (7 + 7x)) = 58x + 121 ((49 + 49x) + 4x * (7 + 7x)) = 58x + 121 (49 + 49x + (7 * 4x + 7x * 4x)) = 58x + 121 (49 + 49x + (28x + 28x2)) = 58x + 121 Combine like terms: 49x + 28x = 77x (49 + 77x + 28x2) = 58x + 121 Reorder the terms: 49 + 77x + 28x2 = 121 + 58x Solving 49 + 77x + 28x2 = 121 + 58x Solving for variable 'x'. Reorder the terms: 49 + -121 + 77x + -58x + 28x2 = 121 + 58x + -121 + -58x Combine like terms: 49 + -121 = -72 -72 + 77x + -58x + 28x2 = 121 + 58x + -121 + -58x Combine like terms: 77x + -58x = 19x -72 + 19x + 28x2 = 121 + 58x + -121 + -58x Reorder the terms: -72 + 19x + 28x2 = 121 + -121 + 58x + -58x Combine like terms: 121 + -121 = 0 -72 + 19x + 28x2 = 0 + 58x + -58x -72 + 19x + 28x2 = 58x + -58x Combine like terms: 58x + -58x = 0 -72 + 19x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -2.571428571 + 0.6785714286x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + 0.6785714286x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + 0.6785714286x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + 0.6785714286x + x2 = 0 + 2.571428571 0.6785714286x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 0.6785714286x + x2 = 2.571428571 The x term is 0.6785714286x. Take half its coefficient (0.3392857143). Square it (0.1151147959) and add it to both sides. Add '0.1151147959' to each side of the equation. 0.6785714286x + 0.1151147959 + x2 = 2.571428571 + 0.1151147959 Reorder the terms: 0.1151147959 + 0.6785714286x + x2 = 2.571428571 + 0.1151147959 Combine like terms: 2.571428571 + 0.1151147959 = 2.6865433669 0.1151147959 + 0.6785714286x + x2 = 2.6865433669 Factor a perfect square on the left side: (x + 0.3392857143)(x + 0.3392857143) = 2.6865433669 Calculate the square root of the right side: 1.639067835 Break this problem into two subproblems by setting (x + 0.3392857143) equal to 1.639067835 and -1.639067835.Subproblem 1
x + 0.3392857143 = 1.639067835 Simplifying x + 0.3392857143 = 1.639067835 Reorder the terms: 0.3392857143 + x = 1.639067835 Solving 0.3392857143 + x = 1.639067835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3392857143' to each side of the equation. 0.3392857143 + -0.3392857143 + x = 1.639067835 + -0.3392857143 Combine like terms: 0.3392857143 + -0.3392857143 = 0.0000000000 0.0000000000 + x = 1.639067835 + -0.3392857143 x = 1.639067835 + -0.3392857143 Combine like terms: 1.639067835 + -0.3392857143 = 1.2997821207 x = 1.2997821207 Simplifying x = 1.2997821207Subproblem 2
x + 0.3392857143 = -1.639067835 Simplifying x + 0.3392857143 = -1.639067835 Reorder the terms: 0.3392857143 + x = -1.639067835 Solving 0.3392857143 + x = -1.639067835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3392857143' to each side of the equation. 0.3392857143 + -0.3392857143 + x = -1.639067835 + -0.3392857143 Combine like terms: 0.3392857143 + -0.3392857143 = 0.0000000000 0.0000000000 + x = -1.639067835 + -0.3392857143 x = -1.639067835 + -0.3392857143 Combine like terms: -1.639067835 + -0.3392857143 = -1.9783535493 x = -1.9783535493 Simplifying x = -1.9783535493Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2997821207, -1.9783535493}
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