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Simplifying 12X(4X + -4) = 4(12X + 6) Reorder the terms: 12X(-4 + 4X) = 4(12X + 6) (-4 * 12X + 4X * 12X) = 4(12X + 6) (-48X + 48X2) = 4(12X + 6) Reorder the terms: -48X + 48X2 = 4(6 + 12X) -48X + 48X2 = (6 * 4 + 12X * 4) -48X + 48X2 = (24 + 48X) Solving -48X + 48X2 = 24 + 48X Solving for variable 'X'. Reorder the terms: -24 + -48X + -48X + 48X2 = 24 + 48X + -24 + -48X Combine like terms: -48X + -48X = -96X -24 + -96X + 48X2 = 24 + 48X + -24 + -48X Reorder the terms: -24 + -96X + 48X2 = 24 + -24 + 48X + -48X Combine like terms: 24 + -24 = 0 -24 + -96X + 48X2 = 0 + 48X + -48X -24 + -96X + 48X2 = 48X + -48X Combine like terms: 48X + -48X = 0 -24 + -96X + 48X2 = 0 Factor out the Greatest Common Factor (GCF), '24'. 24(-1 + -4X + 2X2) = 0 Ignore the factor 24.Subproblem 1
Set the factor '(-1 + -4X + 2X2)' equal to zero and attempt to solve: Simplifying -1 + -4X + 2X2 = 0 Solving -1 + -4X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2X + X2 = 0 + 0.5 -2X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2X + X2 = 0.5 The X term is -2X. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2X + 1 + X2 = 0.5 + 1 Reorder the terms: 1 + -2X + X2 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + -2X + X2 = 1.5 Factor a perfect square on the left side: (X + -1)(X + -1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (X + -1) equal to 1.224744871 and -1.224744871.Subproblem 1
X + -1 = 1.224744871 Simplifying X + -1 = 1.224744871 Reorder the terms: -1 + X = 1.224744871 Solving -1 + X = 1.224744871 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + X = 1.224744871 + 1 X = 1.224744871 + 1 Combine like terms: 1.224744871 + 1 = 2.224744871 X = 2.224744871 Simplifying X = 2.224744871Subproblem 2
X + -1 = -1.224744871 Simplifying X + -1 = -1.224744871 Reorder the terms: -1 + X = -1.224744871 Solving -1 + X = -1.224744871 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + X = -1.224744871 + 1 X = -1.224744871 + 1 Combine like terms: -1.224744871 + 1 = -0.224744871 X = -0.224744871 Simplifying X = -0.224744871Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.224744871, -0.224744871}Solution
X = {2.224744871, -0.224744871}
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