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Simplifying 4x + (43x)(3 + -1x) = 5 + x Remove parenthesis around (43x) 4x + 43x(3 + -1x) = 5 + x 4x + (3 * 43x + -1x * 43x) = 5 + x 4x + (129x + -43x2) = 5 + x Combine like terms: 4x + 129x = 133x 133x + -43x2 = 5 + x Solving 133x + -43x2 = 5 + x Solving for variable 'x'. Reorder the terms: -5 + 133x + -1x + -43x2 = 5 + x + -5 + -1x Combine like terms: 133x + -1x = 132x -5 + 132x + -43x2 = 5 + x + -5 + -1x Reorder the terms: -5 + 132x + -43x2 = 5 + -5 + x + -1x Combine like terms: 5 + -5 = 0 -5 + 132x + -43x2 = 0 + x + -1x -5 + 132x + -43x2 = x + -1x Combine like terms: x + -1x = 0 -5 + 132x + -43x2 = 0 Begin completing the square. Divide all terms by -43 the coefficient of the squared term: Divide each side by '-43'. 0.1162790698 + -3.069767442x + x2 = 0 Move the constant term to the right: Add '-0.1162790698' to each side of the equation. 0.1162790698 + -3.069767442x + -0.1162790698 + x2 = 0 + -0.1162790698 Reorder the terms: 0.1162790698 + -0.1162790698 + -3.069767442x + x2 = 0 + -0.1162790698 Combine like terms: 0.1162790698 + -0.1162790698 = 0.0000000000 0.0000000000 + -3.069767442x + x2 = 0 + -0.1162790698 -3.069767442x + x2 = 0 + -0.1162790698 Combine like terms: 0 + -0.1162790698 = -0.1162790698 -3.069767442x + x2 = -0.1162790698 The x term is -3.069767442x. Take half its coefficient (-1.534883721). Square it (2.355868037) and add it to both sides. Add '2.355868037' to each side of the equation. -3.069767442x + 2.355868037 + x2 = -0.1162790698 + 2.355868037 Reorder the terms: 2.355868037 + -3.069767442x + x2 = -0.1162790698 + 2.355868037 Combine like terms: -0.1162790698 + 2.355868037 = 2.2395889672 2.355868037 + -3.069767442x + x2 = 2.2395889672 Factor a perfect square on the left side: (x + -1.534883721)(x + -1.534883721) = 2.2395889672 Calculate the square root of the right side: 1.496525632 Break this problem into two subproblems by setting (x + -1.534883721) equal to 1.496525632 and -1.496525632.Subproblem 1
x + -1.534883721 = 1.496525632 Simplifying x + -1.534883721 = 1.496525632 Reorder the terms: -1.534883721 + x = 1.496525632 Solving -1.534883721 + x = 1.496525632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.534883721' to each side of the equation. -1.534883721 + 1.534883721 + x = 1.496525632 + 1.534883721 Combine like terms: -1.534883721 + 1.534883721 = 0.000000000 0.000000000 + x = 1.496525632 + 1.534883721 x = 1.496525632 + 1.534883721 Combine like terms: 1.496525632 + 1.534883721 = 3.031409353 x = 3.031409353 Simplifying x = 3.031409353Subproblem 2
x + -1.534883721 = -1.496525632 Simplifying x + -1.534883721 = -1.496525632 Reorder the terms: -1.534883721 + x = -1.496525632 Solving -1.534883721 + x = -1.496525632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.534883721' to each side of the equation. -1.534883721 + 1.534883721 + x = -1.496525632 + 1.534883721 Combine like terms: -1.534883721 + 1.534883721 = 0.000000000 0.000000000 + x = -1.496525632 + 1.534883721 x = -1.496525632 + 1.534883721 Combine like terms: -1.496525632 + 1.534883721 = 0.038358089 x = 0.038358089 Simplifying x = 0.038358089Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.031409353, 0.038358089}
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