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Simplifying 2x3 + -9x2 + -24x = 0 Reorder the terms: -24x + -9x2 + 2x3 = 0 Solving -24x + -9x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-24 + -9x + 2x2) = 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 '(-24 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying -24 + -9x + 2x2 = 0 Solving -24 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + -4.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -4.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -4.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -4.5x + x2 = 0 + 12 -4.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -4.5x + x2 = 12 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 12 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 12 + 5.0625 Combine like terms: 12 + 5.0625 = 17.0625 5.0625 + -4.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + -2.25) equal to 4.13067791 and -4.13067791.Subproblem 1
x + -2.25 = 4.13067791 Simplifying x + -2.25 = 4.13067791 Reorder the terms: -2.25 + x = 4.13067791 Solving -2.25 + x = 4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 4.13067791 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 4.13067791 + 2.25 x = 4.13067791 + 2.25 Combine like terms: 4.13067791 + 2.25 = 6.38067791 x = 6.38067791 Simplifying x = 6.38067791Subproblem 2
x + -2.25 = -4.13067791 Simplifying x + -2.25 = -4.13067791 Reorder the terms: -2.25 + x = -4.13067791 Solving -2.25 + x = -4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -4.13067791 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -4.13067791 + 2.25 x = -4.13067791 + 2.25 Combine like terms: -4.13067791 + 2.25 = -1.88067791 x = -1.88067791 Simplifying x = -1.88067791Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.38067791, -1.88067791}Solution
x = {0, 6.38067791, -1.88067791}
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