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Simplifying 12X + 3X2 + -2X3 = 0 Solving 12X + 3X2 + -2X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(12 + 3X + -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 '(12 + 3X + -2X2)' equal to zero and attempt to solve: Simplifying 12 + 3X + -2X2 = 0 Solving 12 + 3X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + -1.5X + X2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.5X + 6 + X2 = 0 + 6 Reorder the terms: -6 + 6 + -1.5X + X2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.5X + X2 = 0 + 6 -1.5X + X2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.5X + X2 = 6 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 = 6 + 0.5625 Reorder the terms: 0.5625 + -1.5X + X2 = 6 + 0.5625 Combine like terms: 6 + 0.5625 = 6.5625 0.5625 + -1.5X + X2 = 6.5625 Factor a perfect square on the left side: (X + -0.75)(X + -0.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (X + -0.75) equal to 2.561737691 and -2.561737691.Subproblem 1
X + -0.75 = 2.561737691 Simplifying X + -0.75 = 2.561737691 Reorder the terms: -0.75 + X = 2.561737691 Solving -0.75 + X = 2.561737691 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 = 2.561737691 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + X = 2.561737691 + 0.75 X = 2.561737691 + 0.75 Combine like terms: 2.561737691 + 0.75 = 3.311737691 X = 3.311737691 Simplifying X = 3.311737691Subproblem 2
X + -0.75 = -2.561737691 Simplifying X + -0.75 = -2.561737691 Reorder the terms: -0.75 + X = -2.561737691 Solving -0.75 + X = -2.561737691 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 = -2.561737691 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + X = -2.561737691 + 0.75 X = -2.561737691 + 0.75 Combine like terms: -2.561737691 + 0.75 = -1.811737691 X = -1.811737691 Simplifying X = -1.811737691Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.311737691, -1.811737691}Solution
X = {0, 3.311737691, -1.811737691}
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