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Simplifying 2x3 + -12x2 + 9x = 0 Reorder the terms: 9x + -12x2 + 2x3 = 0 Solving 9x + -12x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(9 + -12x + 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 '(9 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -12x + 2x2 = 0 Solving 9 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -6x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -6x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -6x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -6x + x2 = 0 + -4.5 -6x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -6x + x2 = -4.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -4.5 + 9 Reorder the terms: 9 + -6x + x2 = -4.5 + 9 Combine like terms: -4.5 + 9 = 4.5 9 + -6x + x2 = 4.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -3) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -3 = 2.121320344 Simplifying x + -3 = 2.121320344 Reorder the terms: -3 + x = 2.121320344 Solving -3 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.121320344 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.121320344 + 3 x = 2.121320344 + 3 Combine like terms: 2.121320344 + 3 = 5.121320344 x = 5.121320344 Simplifying x = 5.121320344Subproblem 2
x + -3 = -2.121320344 Simplifying x + -3 = -2.121320344 Reorder the terms: -3 + x = -2.121320344 Solving -3 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.121320344 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.121320344 + 3 x = -2.121320344 + 3 Combine like terms: -2.121320344 + 3 = 0.878679656 x = 0.878679656 Simplifying x = 0.878679656Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.121320344, 0.878679656}Solution
x = {0, 5.121320344, 0.878679656}
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