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Simplifying 21x3 + -35x2 + 6x = 0 Reorder the terms: 6x + -35x2 + 21x3 = 0 Solving 6x + -35x2 + 21x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + -35x + 21x2) = 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 '(6 + -35x + 21x2)' equal to zero and attempt to solve: Simplifying 6 + -35x + 21x2 = 0 Solving 6 + -35x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.2857142857 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -1.666666667x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -1.666666667x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + -0.2857142857 -1.666666667x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -1.666666667x + x2 = -0.2857142857 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -0.2857142857 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.2857142857 + 0.6944444447 Combine like terms: -0.2857142857 + 0.6944444447 = 0.408730159 0.6944444447 + -1.666666667x + x2 = 0.408730159 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.408730159 Calculate the square root of the right side: 0.639320076 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.639320076 and -0.639320076.Subproblem 1
x + -0.8333333335 = 0.639320076 Simplifying x + -0.8333333335 = 0.639320076 Reorder the terms: -0.8333333335 + x = 0.639320076 Solving -0.8333333335 + x = 0.639320076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.639320076 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.639320076 + 0.8333333335 x = 0.639320076 + 0.8333333335 Combine like terms: 0.639320076 + 0.8333333335 = 1.4726534095 x = 1.4726534095 Simplifying x = 1.4726534095Subproblem 2
x + -0.8333333335 = -0.639320076 Simplifying x + -0.8333333335 = -0.639320076 Reorder the terms: -0.8333333335 + x = -0.639320076 Solving -0.8333333335 + x = -0.639320076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.639320076 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.639320076 + 0.8333333335 x = -0.639320076 + 0.8333333335 Combine like terms: -0.639320076 + 0.8333333335 = 0.1940132575 x = 0.1940132575 Simplifying x = 0.1940132575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4726534095, 0.1940132575}Solution
x = {0, 1.4726534095, 0.1940132575}
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