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Simplifying (6x2 + 7x + -8)(5x) = 0 Reorder the terms: (-8 + 7x + 6x2)(5x) = 0 Remove parenthesis around (5x) (-8 + 7x + 6x2) * 5x = 0 Reorder the terms for easier multiplication: 5x(-8 + 7x + 6x2) = 0 (-8 * 5x + 7x * 5x + 6x2 * 5x) = 0 (-40x + 35x2 + 30x3) = 0 Solving -40x + 35x2 + 30x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(-8 + 7x + 6x2) = 0 Ignore the factor 5.Subproblem 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 '(-8 + 7x + 6x2)' equal to zero and attempt to solve: Simplifying -8 + 7x + 6x2 = 0 Solving -8 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.166666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.166666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.166666667x + x2 = 0 + 1.333333333 1.166666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.166666667x + x2 = 1.333333333 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 = 1.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 1.333333333 + 0.3402777780 Combine like terms: 1.333333333 + 0.3402777780 = 1.673611111 0.3402777780 + 1.166666667x + x2 = 1.673611111 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 1.673611111 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.293681225 and -1.293681225.Subproblem 1
x + 0.5833333335 = 1.293681225 Simplifying x + 0.5833333335 = 1.293681225 Reorder the terms: 0.5833333335 + x = 1.293681225 Solving 0.5833333335 + x = 1.293681225 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 = 1.293681225 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.293681225 + -0.5833333335 x = 1.293681225 + -0.5833333335 Combine like terms: 1.293681225 + -0.5833333335 = 0.7103478915 x = 0.7103478915 Simplifying x = 0.7103478915Subproblem 2
x + 0.5833333335 = -1.293681225 Simplifying x + 0.5833333335 = -1.293681225 Reorder the terms: 0.5833333335 + x = -1.293681225 Solving 0.5833333335 + x = -1.293681225 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 = -1.293681225 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.293681225 + -0.5833333335 x = -1.293681225 + -0.5833333335 Combine like terms: -1.293681225 + -0.5833333335 = -1.8770145585 x = -1.8770145585 Simplifying x = -1.8770145585Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7103478915, -1.8770145585}Solution
x = {0, 0.7103478915, -1.8770145585}
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