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Simplifying -2x3 + 22x2 + 60x = 0 Reorder the terms: 60x + 22x2 + -2x3 = 0 Solving 60x + 22x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(30 + 11x + -1x2) = 0 Ignore the factor 2.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 '(30 + 11x + -1x2)' equal to zero and attempt to solve: Simplifying 30 + 11x + -1x2 = 0 Solving 30 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -11x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -11x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -11x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -11x + x2 = 0 + 30 -11x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -11x + x2 = 30 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 30 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + -11x + x2 = 60.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + -5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + -5.5 = 7.762087348 Simplifying x + -5.5 = 7.762087348 Reorder the terms: -5.5 + x = 7.762087348 Solving -5.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.762087348 + 5.5 x = 7.762087348 + 5.5 Combine like terms: 7.762087348 + 5.5 = 13.262087348 x = 13.262087348 Simplifying x = 13.262087348Subproblem 2
x + -5.5 = -7.762087348 Simplifying x + -5.5 = -7.762087348 Reorder the terms: -5.5 + x = -7.762087348 Solving -5.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.762087348 + 5.5 x = -7.762087348 + 5.5 Combine like terms: -7.762087348 + 5.5 = -2.262087348 x = -2.262087348 Simplifying x = -2.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.262087348, -2.262087348}Solution
x = {0, 13.262087348, -2.262087348}
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