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Simplifying 4x3 + -12x2 = 9x Reorder the terms: -12x2 + 4x3 = 9x Solving -12x2 + 4x3 = 9x Solving for variable 'x'. Reorder the terms: -9x + -12x2 + 4x3 = 9x + -9x Combine like terms: 9x + -9x = 0 -9x + -12x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + -12x + 4x2) = 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 + 4x2)' equal to zero and attempt to solve: Simplifying -9 + -12x + 4x2 = 0 Solving -9 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -3x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -3x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -3x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -3x + x2 = 0 + 2.25 -3x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -3x + x2 = 2.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.25 + 2.25 Combine like terms: 2.25 + 2.25 = 4.5 2.25 + -3x + x2 = 4.5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -1.5) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -1.5 = 2.121320344 Simplifying x + -1.5 = 2.121320344 Reorder the terms: -1.5 + x = 2.121320344 Solving -1.5 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.121320344 + 1.5 x = 2.121320344 + 1.5 Combine like terms: 2.121320344 + 1.5 = 3.621320344 x = 3.621320344 Simplifying x = 3.621320344Subproblem 2
x + -1.5 = -2.121320344 Simplifying x + -1.5 = -2.121320344 Reorder the terms: -1.5 + x = -2.121320344 Solving -1.5 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.121320344 + 1.5 x = -2.121320344 + 1.5 Combine like terms: -2.121320344 + 1.5 = -0.621320344 x = -0.621320344 Simplifying x = -0.621320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.621320344, -0.621320344}Solution
x = {0, 3.621320344, -0.621320344}
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