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Simplifying (X + -3)(X + 2) + -1 = 0 Reorder the terms: (-3 + X)(X + 2) + -1 = 0 Reorder the terms: (-3 + X)(2 + X) + -1 = 0 Multiply (-3 + X) * (2 + X) (-3(2 + X) + X(2 + X)) + -1 = 0 ((2 * -3 + X * -3) + X(2 + X)) + -1 = 0 ((-6 + -3X) + X(2 + X)) + -1 = 0 (-6 + -3X + (2 * X + X * X)) + -1 = 0 (-6 + -3X + (2X + X2)) + -1 = 0 Combine like terms: -3X + 2X = -1X (-6 + -1X + X2) + -1 = 0 Reorder the terms: -6 + -1 + -1X + X2 = 0 Combine like terms: -6 + -1 = -7 -7 + -1X + X2 = 0 Solving -7 + -1X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -1X + 7 + X2 = 0 + 7 Reorder the terms: -7 + 7 + -1X + X2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1X + X2 = 0 + 7 -1X + X2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1X + X2 = 7 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = 7 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + -1X + X2 = 7.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (X + -0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
X + -0.5 = 2.692582404 Simplifying X + -0.5 = 2.692582404 Reorder the terms: -0.5 + X = 2.692582404 Solving -0.5 + X = 2.692582404 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 2.692582404 + 0.5 X = 2.692582404 + 0.5 Combine like terms: 2.692582404 + 0.5 = 3.192582404 X = 3.192582404 Simplifying X = 3.192582404Subproblem 2
X + -0.5 = -2.692582404 Simplifying X + -0.5 = -2.692582404 Reorder the terms: -0.5 + X = -2.692582404 Solving -0.5 + X = -2.692582404 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -2.692582404 + 0.5 X = -2.692582404 + 0.5 Combine like terms: -2.692582404 + 0.5 = -2.192582404 X = -2.192582404 Simplifying X = -2.192582404Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.192582404, -2.192582404}
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