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Simplifying (X + 7)(6 + -1X) = 6 Reorder the terms: (7 + X)(6 + -1X) = 6 Multiply (7 + X) * (6 + -1X) (7(6 + -1X) + X(6 + -1X)) = 6 ((6 * 7 + -1X * 7) + X(6 + -1X)) = 6 ((42 + -7X) + X(6 + -1X)) = 6 (42 + -7X + (6 * X + -1X * X)) = 6 (42 + -7X + (6X + -1X2)) = 6 Combine like terms: -7X + 6X = -1X (42 + -1X + -1X2) = 6 Solving 42 + -1X + -1X2 = 6 Solving for variable 'X'. Reorder the terms: 42 + -6 + -1X + -1X2 = 6 + -6 Combine like terms: 42 + -6 = 36 36 + -1X + -1X2 = 6 + -6 Combine like terms: 6 + -6 = 0 36 + -1X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + X + X2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + X + 36 + X2 = 0 + 36 Reorder the terms: -36 + 36 + X + X2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + X + X2 = 0 + 36 X + X2 = 0 + 36 Combine like terms: 0 + 36 = 36 X + X2 = 36 The X term is X. 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. + 0.25 + X2 = 36 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 1.25 + X2 = 36.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (X + 0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
X + 0.5 = 6.020797289 Simplifying X + 0.5 = 6.020797289 Reorder the terms: 0.5 + X = 6.020797289 Solving 0.5 + X = 6.020797289 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 = 6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 6.020797289 + -0.5 X = 6.020797289 + -0.5 Combine like terms: 6.020797289 + -0.5 = 5.520797289 X = 5.520797289 Simplifying X = 5.520797289Subproblem 2
X + 0.5 = -6.020797289 Simplifying X + 0.5 = -6.020797289 Reorder the terms: 0.5 + X = -6.020797289 Solving 0.5 + X = -6.020797289 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 = -6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -6.020797289 + -0.5 X = -6.020797289 + -0.5 Combine like terms: -6.020797289 + -0.5 = -6.520797289 X = -6.520797289 Simplifying X = -6.520797289Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.520797289, -6.520797289}
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