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Simplifying 6x3 + 7x2 + -56x = 0 Reorder the terms: -56x + 7x2 + 6x3 = 0 Solving -56x + 7x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-56 + 7x + 6x2) = 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 '(-56 + 7x + 6x2)' equal to zero and attempt to solve: Simplifying -56 + 7x + 6x2 = 0 Solving -56 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -9.333333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + 1.166666667x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + 1.166666667x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + 1.166666667x + x2 = 0 + 9.333333333 1.166666667x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 1.166666667x + x2 = 9.333333333 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 9.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 9.333333333 + 0.3402777780 Combine like terms: 9.333333333 + 0.3402777780 = 9.673611111 0.3402777780 + 1.166666667x + x2 = 9.673611111 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 9.673611111 Calculate the square root of the right side: 3.110242934 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 3.110242934 and -3.110242934.Subproblem 1
x + 0.5833333335 = 3.110242934 Simplifying x + 0.5833333335 = 3.110242934 Reorder the terms: 0.5833333335 + x = 3.110242934 Solving 0.5833333335 + x = 3.110242934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 3.110242934 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 3.110242934 + -0.5833333335 x = 3.110242934 + -0.5833333335 Combine like terms: 3.110242934 + -0.5833333335 = 2.5269096005 x = 2.5269096005 Simplifying x = 2.5269096005Subproblem 2
x + 0.5833333335 = -3.110242934 Simplifying x + 0.5833333335 = -3.110242934 Reorder the terms: 0.5833333335 + x = -3.110242934 Solving 0.5833333335 + x = -3.110242934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -3.110242934 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -3.110242934 + -0.5833333335 x = -3.110242934 + -0.5833333335 Combine like terms: -3.110242934 + -0.5833333335 = -3.6935762675 x = -3.6935762675 Simplifying x = -3.6935762675Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5269096005, -3.6935762675}Solution
x = {0, 2.5269096005, -3.6935762675}
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