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Simplifying (X + -0.5)(X + 2) = 0 Reorder the terms: (-0.5 + X)(X + 2) = 0 Reorder the terms: (-0.5 + X)(2 + X) = 0 Multiply (-0.5 + X) * (2 + X) (-0.5(2 + X) + X(2 + X)) = 0 ((2 * -0.5 + X * -0.5) + X(2 + X)) = 0 ((-1 + -0.5X) + X(2 + X)) = 0 (-1 + -0.5X + (2 * X + X * X)) = 0 (-1 + -0.5X + (2X + X2)) = 0 Combine like terms: -0.5X + 2X = 1.5X (-1 + 1.5X + X2) = 0 Solving -1 + 1.5X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.5X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + 1.5X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.5X + X2 = 0 + 1 1.5X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.5X + X2 = 1 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 = 1 + 0.5625 Reorder the terms: 0.5625 + 1.5X + X2 = 1 + 0.5625 Combine like terms: 1 + 0.5625 = 1.5625 0.5625 + 1.5X + X2 = 1.5625 Factor a perfect square on the left side: (X + 0.75)(X + 0.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (X + 0.75) equal to 1.25 and -1.25.Subproblem 1
X + 0.75 = 1.25 Simplifying X + 0.75 = 1.25 Reorder the terms: 0.75 + X = 1.25 Solving 0.75 + X = 1.25 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 = 1.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = 1.25 + -0.75 X = 1.25 + -0.75 Combine like terms: 1.25 + -0.75 = 0.5 X = 0.5 Simplifying X = 0.5Subproblem 2
X + 0.75 = -1.25 Simplifying X + 0.75 = -1.25 Reorder the terms: 0.75 + X = -1.25 Solving 0.75 + X = -1.25 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 = -1.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = -1.25 + -0.75 X = -1.25 + -0.75 Combine like terms: -1.25 + -0.75 = -2 X = -2 Simplifying X = -2Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.5, -2}
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