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Simplifying (2X + -3)(X + 1) = X Reorder the terms: (-3 + 2X)(X + 1) = X Reorder the terms: (-3 + 2X)(1 + X) = X Multiply (-3 + 2X) * (1 + X) (-3(1 + X) + 2X * (1 + X)) = X ((1 * -3 + X * -3) + 2X * (1 + X)) = X ((-3 + -3X) + 2X * (1 + X)) = X (-3 + -3X + (1 * 2X + X * 2X)) = X (-3 + -3X + (2X + 2X2)) = X Combine like terms: -3X + 2X = -1X (-3 + -1X + 2X2) = X Solving -3 + -1X + 2X2 = X Solving for variable 'X'. Reorder the terms: -3 + -1X + -1X + 2X2 = X + -1X Combine like terms: -1X + -1X = -2X -3 + -2X + 2X2 = X + -1X Combine like terms: X + -1X = 0 -3 + -2X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -1X + X2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1X + 1.5 + X2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1X + X2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1X + X2 = 0 + 1.5 -1X + X2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1X + X2 = 1.5 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 = 1.5 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 0.25 + -1X + X2 = 1.75 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (X + -0.5) equal to 1.322875656 and -1.322875656.Subproblem 1
X + -0.5 = 1.322875656 Simplifying X + -0.5 = 1.322875656 Reorder the terms: -0.5 + X = 1.322875656 Solving -0.5 + X = 1.322875656 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 = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 1.322875656 + 0.5 X = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 X = 1.822875656 Simplifying X = 1.822875656Subproblem 2
X + -0.5 = -1.322875656 Simplifying X + -0.5 = -1.322875656 Reorder the terms: -0.5 + X = -1.322875656 Solving -0.5 + X = -1.322875656 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 = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -1.322875656 + 0.5 X = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 X = -0.822875656 Simplifying X = -0.822875656Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.822875656, -0.822875656}
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