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Simplifying (X + 7)(X + 7) = 11 Reorder the terms: (7 + X)(X + 7) = 11 Reorder the terms: (7 + X)(7 + X) = 11 Multiply (7 + X) * (7 + X) (7(7 + X) + X(7 + X)) = 11 ((7 * 7 + X * 7) + X(7 + X)) = 11 ((49 + 7X) + X(7 + X)) = 11 (49 + 7X + (7 * X + X * X)) = 11 (49 + 7X + (7X + X2)) = 11 Combine like terms: 7X + 7X = 14X (49 + 14X + X2) = 11 Solving 49 + 14X + X2 = 11 Solving for variable 'X'. Reorder the terms: 49 + -11 + 14X + X2 = 11 + -11 Combine like terms: 49 + -11 = 38 38 + 14X + X2 = 11 + -11 Combine like terms: 11 + -11 = 0 38 + 14X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + 14X + -38 + X2 = 0 + -38 Reorder the terms: 38 + -38 + 14X + X2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + 14X + X2 = 0 + -38 14X + X2 = 0 + -38 Combine like terms: 0 + -38 = -38 14X + X2 = -38 The X term is 14X. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14X + 49 + X2 = -38 + 49 Reorder the terms: 49 + 14X + X2 = -38 + 49 Combine like terms: -38 + 49 = 11 49 + 14X + X2 = 11 Factor a perfect square on the left side: (X + 7)(X + 7) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (X + 7) equal to 3.31662479 and -3.31662479.Subproblem 1
X + 7 = 3.31662479 Simplifying X + 7 = 3.31662479 Reorder the terms: 7 + X = 3.31662479 Solving 7 + X = 3.31662479 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = 3.31662479 + -7 Combine like terms: 7 + -7 = 0 0 + X = 3.31662479 + -7 X = 3.31662479 + -7 Combine like terms: 3.31662479 + -7 = -3.68337521 X = -3.68337521 Simplifying X = -3.68337521Subproblem 2
X + 7 = -3.31662479 Simplifying X + 7 = -3.31662479 Reorder the terms: 7 + X = -3.31662479 Solving 7 + X = -3.31662479 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = -3.31662479 + -7 Combine like terms: 7 + -7 = 0 0 + X = -3.31662479 + -7 X = -3.31662479 + -7 Combine like terms: -3.31662479 + -7 = -10.31662479 X = -10.31662479 Simplifying X = -10.31662479Solution
The solution to the problem is based on the solutions from the subproblems. X = {-3.68337521, -10.31662479}
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