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Simplifying 12x2 + 29x + -17 = 0 Reorder the terms: -17 + 29x + 12x2 = 0 Solving -17 + 29x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.416666667 + 2.416666667x + x2 = 0 Move the constant term to the right: Add '1.416666667' to each side of the equation. -1.416666667 + 2.416666667x + 1.416666667 + x2 = 0 + 1.416666667 Reorder the terms: -1.416666667 + 1.416666667 + 2.416666667x + x2 = 0 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + 2.416666667x + x2 = 0 + 1.416666667 2.416666667x + x2 = 0 + 1.416666667 Combine like terms: 0 + 1.416666667 = 1.416666667 2.416666667x + x2 = 1.416666667 The x term is 2.416666667x. Take half its coefficient (1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. 2.416666667x + 1.460069446 + x2 = 1.416666667 + 1.460069446 Reorder the terms: 1.460069446 + 2.416666667x + x2 = 1.416666667 + 1.460069446 Combine like terms: 1.416666667 + 1.460069446 = 2.876736113 1.460069446 + 2.416666667x + x2 = 2.876736113 Factor a perfect square on the left side: (x + 1.208333334)(x + 1.208333334) = 2.876736113 Calculate the square root of the right side: 1.69609437 Break this problem into two subproblems by setting (x + 1.208333334) equal to 1.69609437 and -1.69609437.Subproblem 1
x + 1.208333334 = 1.69609437 Simplifying x + 1.208333334 = 1.69609437 Reorder the terms: 1.208333334 + x = 1.69609437 Solving 1.208333334 + x = 1.69609437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = 1.69609437 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = 1.69609437 + -1.208333334 x = 1.69609437 + -1.208333334 Combine like terms: 1.69609437 + -1.208333334 = 0.487761036 x = 0.487761036 Simplifying x = 0.487761036Subproblem 2
x + 1.208333334 = -1.69609437 Simplifying x + 1.208333334 = -1.69609437 Reorder the terms: 1.208333334 + x = -1.69609437 Solving 1.208333334 + x = -1.69609437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = -1.69609437 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = -1.69609437 + -1.208333334 x = -1.69609437 + -1.208333334 Combine like terms: -1.69609437 + -1.208333334 = -2.904427704 x = -2.904427704 Simplifying x = -2.904427704Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.487761036, -2.904427704}
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