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Simplifying 3x2 + 29x + -8.9 = 0 Reorder the terms: -8.9 + 29x + 3x2 = 0 Solving -8.9 + 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'. -2.966666667 + 9.666666667x + x2 = 0 Move the constant term to the right: Add '2.966666667' to each side of the equation. -2.966666667 + 9.666666667x + 2.966666667 + x2 = 0 + 2.966666667 Reorder the terms: -2.966666667 + 2.966666667 + 9.666666667x + x2 = 0 + 2.966666667 Combine like terms: -2.966666667 + 2.966666667 = 0.000000000 0.000000000 + 9.666666667x + x2 = 0 + 2.966666667 9.666666667x + x2 = 0 + 2.966666667 Combine like terms: 0 + 2.966666667 = 2.966666667 9.666666667x + x2 = 2.966666667 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 = 2.966666667 + 23.36111112 Reorder the terms: 23.36111112 + 9.666666667x + x2 = 2.966666667 + 23.36111112 Combine like terms: 2.966666667 + 23.36111112 = 26.327777787 23.36111112 + 9.666666667x + x2 = 26.327777787 Factor a perfect square on the left side: (x + 4.833333334)(x + 4.833333334) = 26.327777787 Calculate the square root of the right side: 5.131060104 Break this problem into two subproblems by setting (x + 4.833333334) equal to 5.131060104 and -5.131060104.Subproblem 1
x + 4.833333334 = 5.131060104 Simplifying x + 4.833333334 = 5.131060104 Reorder the terms: 4.833333334 + x = 5.131060104 Solving 4.833333334 + x = 5.131060104 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 = 5.131060104 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = 5.131060104 + -4.833333334 x = 5.131060104 + -4.833333334 Combine like terms: 5.131060104 + -4.833333334 = 0.29772677 x = 0.29772677 Simplifying x = 0.29772677Subproblem 2
x + 4.833333334 = -5.131060104 Simplifying x + 4.833333334 = -5.131060104 Reorder the terms: 4.833333334 + x = -5.131060104 Solving 4.833333334 + x = -5.131060104 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 = -5.131060104 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = -5.131060104 + -4.833333334 x = -5.131060104 + -4.833333334 Combine like terms: -5.131060104 + -4.833333334 = -9.964393438 x = -9.964393438 Simplifying x = -9.964393438Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.29772677, -9.964393438}
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