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Simplifying (2X + -3)(2X + -3) = 6 Reorder the terms: (-3 + 2X)(2X + -3) = 6 Reorder the terms: (-3 + 2X)(-3 + 2X) = 6 Multiply (-3 + 2X) * (-3 + 2X) (-3(-3 + 2X) + 2X * (-3 + 2X)) = 6 ((-3 * -3 + 2X * -3) + 2X * (-3 + 2X)) = 6 ((9 + -6X) + 2X * (-3 + 2X)) = 6 (9 + -6X + (-3 * 2X + 2X * 2X)) = 6 (9 + -6X + (-6X + 4X2)) = 6 Combine like terms: -6X + -6X = -12X (9 + -12X + 4X2) = 6 Solving 9 + -12X + 4X2 = 6 Solving for variable 'X'. Reorder the terms: 9 + -6 + -12X + 4X2 = 6 + -6 Combine like terms: 9 + -6 = 3 3 + -12X + 4X2 = 6 + -6 Combine like terms: 6 + -6 = 0 3 + -12X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -3X + X2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -3X + -0.75 + X2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -3X + X2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -3X + X2 = 0 + -0.75 -3X + X2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -3X + X2 = -0.75 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 = -0.75 + 2.25 Reorder the terms: 2.25 + -3X + X2 = -0.75 + 2.25 Combine like terms: -0.75 + 2.25 = 1.5 2.25 + -3X + X2 = 1.5 Factor a perfect square on the left side: (X + -1.5)(X + -1.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (X + -1.5) equal to 1.224744871 and -1.224744871.Subproblem 1
X + -1.5 = 1.224744871 Simplifying X + -1.5 = 1.224744871 Reorder the terms: -1.5 + X = 1.224744871 Solving -1.5 + X = 1.224744871 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 = 1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = 1.224744871 + 1.5 X = 1.224744871 + 1.5 Combine like terms: 1.224744871 + 1.5 = 2.724744871 X = 2.724744871 Simplifying X = 2.724744871Subproblem 2
X + -1.5 = -1.224744871 Simplifying X + -1.5 = -1.224744871 Reorder the terms: -1.5 + X = -1.224744871 Solving -1.5 + X = -1.224744871 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 = -1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = -1.224744871 + 1.5 X = -1.224744871 + 1.5 Combine like terms: -1.224744871 + 1.5 = 0.275255129 X = 0.275255129 Simplifying X = 0.275255129Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.724744871, 0.275255129}
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