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Simplifying 3x * x + 29x = 300 Multiply x * x 3x2 + 29x = 300 Reorder the terms: 29x + 3x2 = 300 Solving 29x + 3x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 29x + 3x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 29x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -100 + 9.666666667x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 9.666666667x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 9.666666667x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 9.666666667x + x2 = 0 + 100 9.666666667x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 9.666666667x + x2 = 100 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 = 100 + 23.36111112 Reorder the terms: 23.36111112 + 9.666666667x + x2 = 100 + 23.36111112 Combine like terms: 100 + 23.36111112 = 123.36111112 23.36111112 + 9.666666667x + x2 = 123.36111112 Factor a perfect square on the left side: (x + 4.833333334)(x + 4.833333334) = 123.36111112 Calculate the square root of the right side: 11.106804721 Break this problem into two subproblems by setting (x + 4.833333334) equal to 11.106804721 and -11.106804721.Subproblem 1
x + 4.833333334 = 11.106804721 Simplifying x + 4.833333334 = 11.106804721 Reorder the terms: 4.833333334 + x = 11.106804721 Solving 4.833333334 + x = 11.106804721 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 = 11.106804721 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = 11.106804721 + -4.833333334 x = 11.106804721 + -4.833333334 Combine like terms: 11.106804721 + -4.833333334 = 6.273471387 x = 6.273471387 Simplifying x = 6.273471387Subproblem 2
x + 4.833333334 = -11.106804721 Simplifying x + 4.833333334 = -11.106804721 Reorder the terms: 4.833333334 + x = -11.106804721 Solving 4.833333334 + x = -11.106804721 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 = -11.106804721 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = -11.106804721 + -4.833333334 x = -11.106804721 + -4.833333334 Combine like terms: -11.106804721 + -4.833333334 = -15.940138055 x = -15.940138055 Simplifying x = -15.940138055Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.273471387, -15.940138055}
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