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Simplifying 2x + 7x2 + -9x + 21x3 + 5x = 0 Reorder the terms: 2x + -9x + 5x + 7x2 + 21x3 = 0 Combine like terms: 2x + -9x = -7x -7x + 5x + 7x2 + 21x3 = 0 Combine like terms: -7x + 5x = -2x -2x + 7x2 + 21x3 = 0 Solving -2x + 7x2 + 21x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + 7x + 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 '(-2 + 7x + 21x2)' equal to zero and attempt to solve: Simplifying -2 + 7x + 21x2 = 0 Solving -2 + 7x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.09523809524 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.09523809524' to each side of the equation. -0.09523809524 + 0.3333333333x + 0.09523809524 + x2 = 0 + 0.09523809524 Reorder the terms: -0.09523809524 + 0.09523809524 + 0.3333333333x + x2 = 0 + 0.09523809524 Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000 0.00000000000 + 0.3333333333x + x2 = 0 + 0.09523809524 0.3333333333x + x2 = 0 + 0.09523809524 Combine like terms: 0 + 0.09523809524 = 0.09523809524 0.3333333333x + x2 = 0.09523809524 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.09523809524 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.09523809524 + 0.02777777779 Combine like terms: 0.09523809524 + 0.02777777779 = 0.12301587303 0.02777777779 + 0.3333333333x + x2 = 0.12301587303 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.12301587303 Calculate the square root of the right side: 0.350736187 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.350736187 and -0.350736187.Subproblem 1
x + 0.1666666667 = 0.350736187 Simplifying x + 0.1666666667 = 0.350736187 Reorder the terms: 0.1666666667 + x = 0.350736187 Solving 0.1666666667 + x = 0.350736187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.350736187 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.350736187 + -0.1666666667 x = 0.350736187 + -0.1666666667 Combine like terms: 0.350736187 + -0.1666666667 = 0.1840695203 x = 0.1840695203 Simplifying x = 0.1840695203Subproblem 2
x + 0.1666666667 = -0.350736187 Simplifying x + 0.1666666667 = -0.350736187 Reorder the terms: 0.1666666667 + x = -0.350736187 Solving 0.1666666667 + x = -0.350736187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.350736187 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.350736187 + -0.1666666667 x = -0.350736187 + -0.1666666667 Combine like terms: -0.350736187 + -0.1666666667 = -0.5174028537 x = -0.5174028537 Simplifying x = -0.5174028537Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1840695203, -0.5174028537}Solution
x = {0, 0.1840695203, -0.5174028537}
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