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Simplifying (3x + 2)(34x + 99) = 4 Reorder the terms: (2 + 3x)(34x + 99) = 4 Reorder the terms: (2 + 3x)(99 + 34x) = 4 Multiply (2 + 3x) * (99 + 34x) (2(99 + 34x) + 3x * (99 + 34x)) = 4 ((99 * 2 + 34x * 2) + 3x * (99 + 34x)) = 4 ((198 + 68x) + 3x * (99 + 34x)) = 4 (198 + 68x + (99 * 3x + 34x * 3x)) = 4 (198 + 68x + (297x + 102x2)) = 4 Combine like terms: 68x + 297x = 365x (198 + 365x + 102x2) = 4 Solving 198 + 365x + 102x2 = 4 Solving for variable 'x'. Reorder the terms: 198 + -4 + 365x + 102x2 = 4 + -4 Combine like terms: 198 + -4 = 194 194 + 365x + 102x2 = 4 + -4 Combine like terms: 4 + -4 = 0 194 + 365x + 102x2 = 0 Begin completing the square. Divide all terms by 102 the coefficient of the squared term: Divide each side by '102'. 1.901960784 + 3.578431373x + x2 = 0 Move the constant term to the right: Add '-1.901960784' to each side of the equation. 1.901960784 + 3.578431373x + -1.901960784 + x2 = 0 + -1.901960784 Reorder the terms: 1.901960784 + -1.901960784 + 3.578431373x + x2 = 0 + -1.901960784 Combine like terms: 1.901960784 + -1.901960784 = 0.000000000 0.000000000 + 3.578431373x + x2 = 0 + -1.901960784 3.578431373x + x2 = 0 + -1.901960784 Combine like terms: 0 + -1.901960784 = -1.901960784 3.578431373x + x2 = -1.901960784 The x term is 3.578431373x. Take half its coefficient (1.789215687). Square it (3.201292775) and add it to both sides. Add '3.201292775' to each side of the equation. 3.578431373x + 3.201292775 + x2 = -1.901960784 + 3.201292775 Reorder the terms: 3.201292775 + 3.578431373x + x2 = -1.901960784 + 3.201292775 Combine like terms: -1.901960784 + 3.201292775 = 1.299331991 3.201292775 + 3.578431373x + x2 = 1.299331991 Factor a perfect square on the left side: (x + 1.789215687)(x + 1.789215687) = 1.299331991 Calculate the square root of the right side: 1.139882446 Break this problem into two subproblems by setting (x + 1.789215687) equal to 1.139882446 and -1.139882446.Subproblem 1
x + 1.789215687 = 1.139882446 Simplifying x + 1.789215687 = 1.139882446 Reorder the terms: 1.789215687 + x = 1.139882446 Solving 1.789215687 + x = 1.139882446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.789215687' to each side of the equation. 1.789215687 + -1.789215687 + x = 1.139882446 + -1.789215687 Combine like terms: 1.789215687 + -1.789215687 = 0.000000000 0.000000000 + x = 1.139882446 + -1.789215687 x = 1.139882446 + -1.789215687 Combine like terms: 1.139882446 + -1.789215687 = -0.649333241 x = -0.649333241 Simplifying x = -0.649333241Subproblem 2
x + 1.789215687 = -1.139882446 Simplifying x + 1.789215687 = -1.139882446 Reorder the terms: 1.789215687 + x = -1.139882446 Solving 1.789215687 + x = -1.139882446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.789215687' to each side of the equation. 1.789215687 + -1.789215687 + x = -1.139882446 + -1.789215687 Combine like terms: 1.789215687 + -1.789215687 = 0.000000000 0.000000000 + x = -1.139882446 + -1.789215687 x = -1.139882446 + -1.789215687 Combine like terms: -1.139882446 + -1.789215687 = -2.929098133 x = -2.929098133 Simplifying x = -2.929098133Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.649333241, -2.929098133}
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