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Simplifying 2x3 + 13x2 + -48x = 0 Reorder the terms: -48x + 13x2 + 2x3 = 0 Solving -48x + 13x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-48 + 13x + 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 '(-48 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying -48 + 13x + 2x2 = 0 Solving -48 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + 6.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 6.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 6.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 6.5x + x2 = 0 + 24 6.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 6.5x + x2 = 24 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 24 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 24 + 10.5625 Combine like terms: 24 + 10.5625 = 34.5625 10.5625 + 6.5x + x2 = 34.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (x + 3.25) equal to 5.878988008 and -5.878988008.Subproblem 1
x + 3.25 = 5.878988008 Simplifying x + 3.25 = 5.878988008 Reorder the terms: 3.25 + x = 5.878988008 Solving 3.25 + x = 5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 5.878988008 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 5.878988008 + -3.25 x = 5.878988008 + -3.25 Combine like terms: 5.878988008 + -3.25 = 2.628988008 x = 2.628988008 Simplifying x = 2.628988008Subproblem 2
x + 3.25 = -5.878988008 Simplifying x + 3.25 = -5.878988008 Reorder the terms: 3.25 + x = -5.878988008 Solving 3.25 + x = -5.878988008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -5.878988008 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -5.878988008 + -3.25 x = -5.878988008 + -3.25 Combine like terms: -5.878988008 + -3.25 = -9.128988008 x = -9.128988008 Simplifying x = -9.128988008Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.628988008, -9.128988008}Solution
x = {0, 2.628988008, -9.128988008}
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