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Simplifying (X + -5)(2X + -4) = 5 Reorder the terms: (-5 + X)(2X + -4) = 5 Reorder the terms: (-5 + X)(-4 + 2X) = 5 Multiply (-5 + X) * (-4 + 2X) (-5(-4 + 2X) + X(-4 + 2X)) = 5 ((-4 * -5 + 2X * -5) + X(-4 + 2X)) = 5 ((20 + -10X) + X(-4 + 2X)) = 5 (20 + -10X + (-4 * X + 2X * X)) = 5 (20 + -10X + (-4X + 2X2)) = 5 Combine like terms: -10X + -4X = -14X (20 + -14X + 2X2) = 5 Solving 20 + -14X + 2X2 = 5 Solving for variable 'X'. Reorder the terms: 20 + -5 + -14X + 2X2 = 5 + -5 Combine like terms: 20 + -5 = 15 15 + -14X + 2X2 = 5 + -5 Combine like terms: 5 + -5 = 0 15 + -14X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -7X + X2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -7X + -7.5 + X2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -7X + X2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -7X + X2 = 0 + -7.5 -7X + X2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -7X + X2 = -7.5 The X term is -7X. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7X + 12.25 + X2 = -7.5 + 12.25 Reorder the terms: 12.25 + -7X + X2 = -7.5 + 12.25 Combine like terms: -7.5 + 12.25 = 4.75 12.25 + -7X + X2 = 4.75 Factor a perfect square on the left side: (X + -3.5)(X + -3.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (X + -3.5) equal to 2.179449472 and -2.179449472.Subproblem 1
X + -3.5 = 2.179449472 Simplifying X + -3.5 = 2.179449472 Reorder the terms: -3.5 + X = 2.179449472 Solving -3.5 + X = 2.179449472 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = 2.179449472 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = 2.179449472 + 3.5 X = 2.179449472 + 3.5 Combine like terms: 2.179449472 + 3.5 = 5.679449472 X = 5.679449472 Simplifying X = 5.679449472Subproblem 2
X + -3.5 = -2.179449472 Simplifying X + -3.5 = -2.179449472 Reorder the terms: -3.5 + X = -2.179449472 Solving -3.5 + X = -2.179449472 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = -2.179449472 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = -2.179449472 + 3.5 X = -2.179449472 + 3.5 Combine like terms: -2.179449472 + 3.5 = 1.320550528 X = 1.320550528 Simplifying X = 1.320550528Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.679449472, 1.320550528}
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