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Simplifying 24x3 + 36x2 + -72x = 0 Reorder the terms: -72x + 36x2 + 24x3 = 0 Solving -72x + 36x2 + 24x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12x'. 12x(-6 + 3x + 2x2) = 0 Ignore the factor 12.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 '(-6 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying -6 + 3x + 2x2 = 0 Solving -6 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 1.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.5x + x2 = 0 + 3 1.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.5x + x2 = 3 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 3 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3 + 0.5625 Combine like terms: 3 + 0.5625 = 3.5625 0.5625 + 1.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 0.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 0.75 = 1.887458609 Simplifying x + 0.75 = 1.887458609 Reorder the terms: 0.75 + x = 1.887458609 Solving 0.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.887458609 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.887458609 + -0.75 x = 1.887458609 + -0.75 Combine like terms: 1.887458609 + -0.75 = 1.137458609 x = 1.137458609 Simplifying x = 1.137458609Subproblem 2
x + 0.75 = -1.887458609 Simplifying x + 0.75 = -1.887458609 Reorder the terms: 0.75 + x = -1.887458609 Solving 0.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.887458609 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.887458609 + -0.75 x = -1.887458609 + -0.75 Combine like terms: -1.887458609 + -0.75 = -2.637458609 x = -2.637458609 Simplifying x = -2.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.137458609, -2.637458609}Solution
x = {0, 1.137458609, -2.637458609}
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