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Simplifying 30x3 + -47x2 + -14x = 0 Reorder the terms: -14x + -47x2 + 30x3 = 0 Solving -14x + -47x2 + 30x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-14 + -47x + 30x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-14 + -47x + 30x2)' equal to zero and attempt to solve: Simplifying -14 + -47x + 30x2 = 0 Solving -14 + -47x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.4666666667 + -1.566666667x + x2 = 0 Move the constant term to the right: Add '0.4666666667' to each side of the equation. -0.4666666667 + -1.566666667x + 0.4666666667 + x2 = 0 + 0.4666666667 Reorder the terms: -0.4666666667 + 0.4666666667 + -1.566666667x + x2 = 0 + 0.4666666667 Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000 0.0000000000 + -1.566666667x + x2 = 0 + 0.4666666667 -1.566666667x + x2 = 0 + 0.4666666667 Combine like terms: 0 + 0.4666666667 = 0.4666666667 -1.566666667x + x2 = 0.4666666667 The x term is -1.566666667x. Take half its coefficient (-0.7833333335). Square it (0.6136111114) and add it to both sides. Add '0.6136111114' to each side of the equation. -1.566666667x + 0.6136111114 + x2 = 0.4666666667 + 0.6136111114 Reorder the terms: 0.6136111114 + -1.566666667x + x2 = 0.4666666667 + 0.6136111114 Combine like terms: 0.4666666667 + 0.6136111114 = 1.0802777781 0.6136111114 + -1.566666667x + x2 = 1.0802777781 Factor a perfect square on the left side: (x + -0.7833333335)(x + -0.7833333335) = 1.0802777781 Calculate the square root of the right side: 1.039364122 Break this problem into two subproblems by setting (x + -0.7833333335) equal to 1.039364122 and -1.039364122.Subproblem 1
x + -0.7833333335 = 1.039364122 Simplifying x + -0.7833333335 = 1.039364122 Reorder the terms: -0.7833333335 + x = 1.039364122 Solving -0.7833333335 + x = 1.039364122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7833333335' to each side of the equation. -0.7833333335 + 0.7833333335 + x = 1.039364122 + 0.7833333335 Combine like terms: -0.7833333335 + 0.7833333335 = 0.0000000000 0.0000000000 + x = 1.039364122 + 0.7833333335 x = 1.039364122 + 0.7833333335 Combine like terms: 1.039364122 + 0.7833333335 = 1.8226974555 x = 1.8226974555 Simplifying x = 1.8226974555Subproblem 2
x + -0.7833333335 = -1.039364122 Simplifying x + -0.7833333335 = -1.039364122 Reorder the terms: -0.7833333335 + x = -1.039364122 Solving -0.7833333335 + x = -1.039364122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7833333335' to each side of the equation. -0.7833333335 + 0.7833333335 + x = -1.039364122 + 0.7833333335 Combine like terms: -0.7833333335 + 0.7833333335 = 0.0000000000 0.0000000000 + x = -1.039364122 + 0.7833333335 x = -1.039364122 + 0.7833333335 Combine like terms: -1.039364122 + 0.7833333335 = -0.2560307885 x = -0.2560307885 Simplifying x = -0.2560307885Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8226974555, -0.2560307885}Solution
x = {0, 1.8226974555, -0.2560307885}
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