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Simplifying 23x + 3x2 + -1060 = 0 Reorder the terms: -1060 + 23x + 3x2 = 0 Solving -1060 + 23x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -353.3333333 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '353.3333333' to each side of the equation. -353.3333333 + 7.666666667x + 353.3333333 + x2 = 0 + 353.3333333 Reorder the terms: -353.3333333 + 353.3333333 + 7.666666667x + x2 = 0 + 353.3333333 Combine like terms: -353.3333333 + 353.3333333 = 0.0000000 0.0000000 + 7.666666667x + x2 = 0 + 353.3333333 7.666666667x + x2 = 0 + 353.3333333 Combine like terms: 0 + 353.3333333 = 353.3333333 7.666666667x + x2 = 353.3333333 The x term is 7.666666667x. Take half its coefficient (3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. 7.666666667x + 14.69444445 + x2 = 353.3333333 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = 353.3333333 + 14.69444445 Combine like terms: 353.3333333 + 14.69444445 = 368.02777775 14.69444445 + 7.666666667x + x2 = 368.02777775 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 368.02777775 Calculate the square root of the right side: 19.184050087 Break this problem into two subproblems by setting (x + 3.833333334) equal to 19.184050087 and -19.184050087.Subproblem 1
x + 3.833333334 = 19.184050087 Simplifying x + 3.833333334 = 19.184050087 Reorder the terms: 3.833333334 + x = 19.184050087 Solving 3.833333334 + x = 19.184050087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = 19.184050087 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 19.184050087 + -3.833333334 x = 19.184050087 + -3.833333334 Combine like terms: 19.184050087 + -3.833333334 = 15.350716753 x = 15.350716753 Simplifying x = 15.350716753Subproblem 2
x + 3.833333334 = -19.184050087 Simplifying x + 3.833333334 = -19.184050087 Reorder the terms: 3.833333334 + x = -19.184050087 Solving 3.833333334 + x = -19.184050087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.833333334' to each side of the equation. 3.833333334 + -3.833333334 + x = -19.184050087 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -19.184050087 + -3.833333334 x = -19.184050087 + -3.833333334 Combine like terms: -19.184050087 + -3.833333334 = -23.017383421 x = -23.017383421 Simplifying x = -23.017383421Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.350716753, -23.017383421}
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