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Simplifying 4x3 + -21x2 + 4x = 0 Reorder the terms: 4x + -21x2 + 4x3 = 0 Solving 4x + -21x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -21x + 4x2) = 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 '(4 + -21x + 4x2)' equal to zero and attempt to solve: Simplifying 4 + -21x + 4x2 = 0 Solving 4 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -5.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.25x + x2 = 0 + -1 -5.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.25x + x2 = -1 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -1 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -1 + 6.890625 Combine like terms: -1 + 6.890625 = 5.890625 6.890625 + -5.25x + x2 = 5.890625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + -2.625) equal to 2.42706098 and -2.42706098.Subproblem 1
x + -2.625 = 2.42706098 Simplifying x + -2.625 = 2.42706098 Reorder the terms: -2.625 + x = 2.42706098 Solving -2.625 + x = 2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 2.42706098 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.42706098 + 2.625 x = 2.42706098 + 2.625 Combine like terms: 2.42706098 + 2.625 = 5.05206098 x = 5.05206098 Simplifying x = 5.05206098Subproblem 2
x + -2.625 = -2.42706098 Simplifying x + -2.625 = -2.42706098 Reorder the terms: -2.625 + x = -2.42706098 Solving -2.625 + x = -2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -2.42706098 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.42706098 + 2.625 x = -2.42706098 + 2.625 Combine like terms: -2.42706098 + 2.625 = 0.19793902 x = 0.19793902 Simplifying x = 0.19793902Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.05206098, 0.19793902}Solution
x = {0, 5.05206098, 0.19793902}
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