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Simplifying 15x2 + 4x + 3 = 30x2 + 5x Reorder the terms: 3 + 4x + 15x2 = 30x2 + 5x Reorder the terms: 3 + 4x + 15x2 = 5x + 30x2 Solving 3 + 4x + 15x2 = 5x + 30x2 Solving for variable 'x'. Reorder the terms: 3 + 4x + -5x + 15x2 + -30x2 = 5x + 30x2 + -5x + -30x2 Combine like terms: 4x + -5x = -1x 3 + -1x + 15x2 + -30x2 = 5x + 30x2 + -5x + -30x2 Combine like terms: 15x2 + -30x2 = -15x2 3 + -1x + -15x2 = 5x + 30x2 + -5x + -30x2 Reorder the terms: 3 + -1x + -15x2 = 5x + -5x + 30x2 + -30x2 Combine like terms: 5x + -5x = 0 3 + -1x + -15x2 = 0 + 30x2 + -30x2 3 + -1x + -15x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 3 + -1x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.2 + 0.06666666667x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.06666666667x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.06666666667x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.06666666667x + x2 = 0 + 0.2 0.06666666667x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.06666666667x + x2 = 0.2 The x term is 0.06666666667x. Take half its coefficient (0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. 0.06666666667x + 0.001111111112 + x2 = 0.2 + 0.001111111112 Reorder the terms: 0.001111111112 + 0.06666666667x + x2 = 0.2 + 0.001111111112 Combine like terms: 0.2 + 0.001111111112 = 0.201111111112 0.001111111112 + 0.06666666667x + x2 = 0.201111111112 Factor a perfect square on the left side: (x + 0.03333333334)(x + 0.03333333334) = 0.201111111112 Calculate the square root of the right side: 0.448454135 Break this problem into two subproblems by setting (x + 0.03333333334) equal to 0.448454135 and -0.448454135.Subproblem 1
x + 0.03333333334 = 0.448454135 Simplifying x + 0.03333333334 = 0.448454135 Reorder the terms: 0.03333333334 + x = 0.448454135 Solving 0.03333333334 + x = 0.448454135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03333333334' to each side of the equation. 0.03333333334 + -0.03333333334 + x = 0.448454135 + -0.03333333334 Combine like terms: 0.03333333334 + -0.03333333334 = 0.00000000000 0.00000000000 + x = 0.448454135 + -0.03333333334 x = 0.448454135 + -0.03333333334 Combine like terms: 0.448454135 + -0.03333333334 = 0.41512080166 x = 0.41512080166 Simplifying x = 0.41512080166Subproblem 2
x + 0.03333333334 = -0.448454135 Simplifying x + 0.03333333334 = -0.448454135 Reorder the terms: 0.03333333334 + x = -0.448454135 Solving 0.03333333334 + x = -0.448454135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03333333334' to each side of the equation. 0.03333333334 + -0.03333333334 + x = -0.448454135 + -0.03333333334 Combine like terms: 0.03333333334 + -0.03333333334 = 0.00000000000 0.00000000000 + x = -0.448454135 + -0.03333333334 x = -0.448454135 + -0.03333333334 Combine like terms: -0.448454135 + -0.03333333334 = -0.48178746834 x = -0.48178746834 Simplifying x = -0.48178746834Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.41512080166, -0.48178746834}
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