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Simplifying 3x2 + -29x + 9 = 0 Reorder the terms: 9 + -29x + 3x2 = 0 Solving 9 + -29x + 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'. 3 + -9.666666667x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -9.666666667x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -9.666666667x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -9.666666667x + x2 = 0 + -3 -9.666666667x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -9.666666667x + x2 = -3 The x term is -9.666666667x. Take half its coefficient (-4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. -9.666666667x + 23.36111112 + x2 = -3 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667x + x2 = -3 + 23.36111112 Combine like terms: -3 + 23.36111112 = 20.36111112 23.36111112 + -9.666666667x + x2 = 20.36111112 Factor a perfect square on the left side: (x + -4.833333334)(x + -4.833333334) = 20.36111112 Calculate the square root of the right side: 4.512328791 Break this problem into two subproblems by setting (x + -4.833333334) equal to 4.512328791 and -4.512328791.Subproblem 1
x + -4.833333334 = 4.512328791 Simplifying x + -4.833333334 = 4.512328791 Reorder the terms: -4.833333334 + x = 4.512328791 Solving -4.833333334 + x = 4.512328791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = 4.512328791 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 4.512328791 + 4.833333334 x = 4.512328791 + 4.833333334 Combine like terms: 4.512328791 + 4.833333334 = 9.345662125 x = 9.345662125 Simplifying x = 9.345662125Subproblem 2
x + -4.833333334 = -4.512328791 Simplifying x + -4.833333334 = -4.512328791 Reorder the terms: -4.833333334 + x = -4.512328791 Solving -4.833333334 + x = -4.512328791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = -4.512328791 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -4.512328791 + 4.833333334 x = -4.512328791 + 4.833333334 Combine like terms: -4.512328791 + 4.833333334 = 0.321004543 x = 0.321004543 Simplifying x = 0.321004543Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.345662125, 0.321004543}
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