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Simplifying 20x3 + -24x2 + -48x = 0 Reorder the terms: -48x + -24x2 + 20x3 = 0 Solving -48x + -24x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-12 + -6x + 5x2) = 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 '(-12 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying -12 + -6x + 5x2 = 0 Solving -12 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -1.2x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -1.2x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -1.2x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -1.2x + x2 = 0 + 2.4 -1.2x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -1.2x + x2 = 2.4 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 2.4 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 2.4 + 0.36 Combine like terms: 2.4 + 0.36 = 2.76 0.36 + -1.2x + x2 = 2.76 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (x + -0.6) equal to 1.661324773 and -1.661324773.Subproblem 1
x + -0.6 = 1.661324773 Simplifying x + -0.6 = 1.661324773 Reorder the terms: -0.6 + x = 1.661324773 Solving -0.6 + x = 1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.661324773 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.661324773 + 0.6 x = 1.661324773 + 0.6 Combine like terms: 1.661324773 + 0.6 = 2.261324773 x = 2.261324773 Simplifying x = 2.261324773Subproblem 2
x + -0.6 = -1.661324773 Simplifying x + -0.6 = -1.661324773 Reorder the terms: -0.6 + x = -1.661324773 Solving -0.6 + x = -1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.661324773 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.661324773 + 0.6 x = -1.661324773 + 0.6 Combine like terms: -1.661324773 + 0.6 = -1.061324773 x = -1.061324773 Simplifying x = -1.061324773Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.261324773, -1.061324773}Solution
x = {0, 2.261324773, -1.061324773}
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