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Simplifying 8x3 + -39x2 + 20x = 0 Reorder the terms: 20x + -39x2 + 8x3 = 0 Solving 20x + -39x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(20 + -39x + 8x2) = 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 '(20 + -39x + 8x2)' equal to zero and attempt to solve: Simplifying 20 + -39x + 8x2 = 0 Solving 20 + -39x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.5 + -4.875x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -4.875x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -4.875x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -4.875x + x2 = 0 + -2.5 -4.875x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -4.875x + x2 = -2.5 The x term is -4.875x. Take half its coefficient (-2.4375). Square it (5.94140625) and add it to both sides. Add '5.94140625' to each side of the equation. -4.875x + 5.94140625 + x2 = -2.5 + 5.94140625 Reorder the terms: 5.94140625 + -4.875x + x2 = -2.5 + 5.94140625 Combine like terms: -2.5 + 5.94140625 = 3.44140625 5.94140625 + -4.875x + x2 = 3.44140625 Factor a perfect square on the left side: (x + -2.4375)(x + -2.4375) = 3.44140625 Calculate the square root of the right side: 1.85510276 Break this problem into two subproblems by setting (x + -2.4375) equal to 1.85510276 and -1.85510276.Subproblem 1
x + -2.4375 = 1.85510276 Simplifying x + -2.4375 = 1.85510276 Reorder the terms: -2.4375 + x = 1.85510276 Solving -2.4375 + x = 1.85510276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = 1.85510276 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = 1.85510276 + 2.4375 x = 1.85510276 + 2.4375 Combine like terms: 1.85510276 + 2.4375 = 4.29260276 x = 4.29260276 Simplifying x = 4.29260276Subproblem 2
x + -2.4375 = -1.85510276 Simplifying x + -2.4375 = -1.85510276 Reorder the terms: -2.4375 + x = -1.85510276 Solving -2.4375 + x = -1.85510276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = -1.85510276 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = -1.85510276 + 2.4375 x = -1.85510276 + 2.4375 Combine like terms: -1.85510276 + 2.4375 = 0.58239724 x = 0.58239724 Simplifying x = 0.58239724Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.29260276, 0.58239724}Solution
x = {0, 4.29260276, 0.58239724}
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