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Simplifying 3x2 + -29x + -30 = 0 Reorder the terms: -30 + -29x + 3x2 = 0 Solving -30 + -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'. -10 + -9.666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -9.666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -9.666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -9.666666667x + x2 = 0 + 10 -9.666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -9.666666667x + x2 = 10 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 = 10 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667x + x2 = 10 + 23.36111112 Combine like terms: 10 + 23.36111112 = 33.36111112 23.36111112 + -9.666666667x + x2 = 33.36111112 Factor a perfect square on the left side: (x + -4.833333334)(x + -4.833333334) = 33.36111112 Calculate the square root of the right side: 5.775907818 Break this problem into two subproblems by setting (x + -4.833333334) equal to 5.775907818 and -5.775907818.Subproblem 1
x + -4.833333334 = 5.775907818 Simplifying x + -4.833333334 = 5.775907818 Reorder the terms: -4.833333334 + x = 5.775907818 Solving -4.833333334 + x = 5.775907818 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 = 5.775907818 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 5.775907818 + 4.833333334 x = 5.775907818 + 4.833333334 Combine like terms: 5.775907818 + 4.833333334 = 10.609241152 x = 10.609241152 Simplifying x = 10.609241152Subproblem 2
x + -4.833333334 = -5.775907818 Simplifying x + -4.833333334 = -5.775907818 Reorder the terms: -4.833333334 + x = -5.775907818 Solving -4.833333334 + x = -5.775907818 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 = -5.775907818 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -5.775907818 + 4.833333334 x = -5.775907818 + 4.833333334 Combine like terms: -5.775907818 + 4.833333334 = -0.942574484 x = -0.942574484 Simplifying x = -0.942574484Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.609241152, -0.942574484}
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