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Simplifying 8x3 + -20x2 + 4x = 0 Reorder the terms: 4x + -20x2 + 8x3 = 0 Solving 4x + -20x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(1 + -5x + 2x2) = 0 Ignore the factor 4.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 '(1 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -5x + 2x2 = 0 Solving 1 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -2.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -2.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2.5x + x2 = 0 + -0.5 -2.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -2.5x + x2 = -0.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.5 + 1.5625 Combine like terms: -0.5 + 1.5625 = 1.0625 1.5625 + -2.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -1.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x + -1.25 = 1.030776406 Simplifying x + -1.25 = 1.030776406 Reorder the terms: -1.25 + x = 1.030776406 Solving -1.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.030776406 + 1.25 x = 1.030776406 + 1.25 Combine like terms: 1.030776406 + 1.25 = 2.280776406 x = 2.280776406 Simplifying x = 2.280776406Subproblem 2
x + -1.25 = -1.030776406 Simplifying x + -1.25 = -1.030776406 Reorder the terms: -1.25 + x = -1.030776406 Solving -1.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.030776406 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.030776406 + 1.25 x = -1.030776406 + 1.25 Combine like terms: -1.030776406 + 1.25 = 0.219223594 x = 0.219223594 Simplifying x = 0.219223594Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.280776406, 0.219223594}Solution
x = {0, 2.280776406, 0.219223594}
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