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Simplifying (X + 3)(X + 3) = 16 + -2X2 Reorder the terms: (3 + X)(X + 3) = 16 + -2X2 Reorder the terms: (3 + X)(3 + X) = 16 + -2X2 Multiply (3 + X) * (3 + X) (3(3 + X) + X(3 + X)) = 16 + -2X2 ((3 * 3 + X * 3) + X(3 + X)) = 16 + -2X2 ((9 + 3X) + X(3 + X)) = 16 + -2X2 (9 + 3X + (3 * X + X * X)) = 16 + -2X2 (9 + 3X + (3X + X2)) = 16 + -2X2 Combine like terms: 3X + 3X = 6X (9 + 6X + X2) = 16 + -2X2 Solving 9 + 6X + X2 = 16 + -2X2 Solving for variable 'X'. Reorder the terms: 9 + -16 + 6X + X2 + 2X2 = 16 + -2X2 + -16 + 2X2 Combine like terms: 9 + -16 = -7 -7 + 6X + X2 + 2X2 = 16 + -2X2 + -16 + 2X2 Combine like terms: X2 + 2X2 = 3X2 -7 + 6X + 3X2 = 16 + -2X2 + -16 + 2X2 Reorder the terms: -7 + 6X + 3X2 = 16 + -16 + -2X2 + 2X2 Combine like terms: 16 + -16 = 0 -7 + 6X + 3X2 = 0 + -2X2 + 2X2 -7 + 6X + 3X2 = -2X2 + 2X2 Combine like terms: -2X2 + 2X2 = 0 -7 + 6X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + 2X + X2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 2X + 2.333333333 + X2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 2X + X2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 2X + X2 = 0 + 2.333333333 2X + X2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 2X + X2 = 2.333333333 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 2.333333333 + 1 Reorder the terms: 1 + 2X + X2 = 2.333333333 + 1 Combine like terms: 2.333333333 + 1 = 3.333333333 1 + 2X + X2 = 3.333333333 Factor a perfect square on the left side: (X + 1)(X + 1) = 3.333333333 Calculate the square root of the right side: 1.825741858 Break this problem into two subproblems by setting (X + 1) equal to 1.825741858 and -1.825741858.Subproblem 1
X + 1 = 1.825741858 Simplifying X + 1 = 1.825741858 Reorder the terms: 1 + X = 1.825741858 Solving 1 + X = 1.825741858 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 1.825741858 + -1 Combine like terms: 1 + -1 = 0 0 + X = 1.825741858 + -1 X = 1.825741858 + -1 Combine like terms: 1.825741858 + -1 = 0.825741858 X = 0.825741858 Simplifying X = 0.825741858Subproblem 2
X + 1 = -1.825741858 Simplifying X + 1 = -1.825741858 Reorder the terms: 1 + X = -1.825741858 Solving 1 + X = -1.825741858 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -1.825741858 + -1 Combine like terms: 1 + -1 = 0 0 + X = -1.825741858 + -1 X = -1.825741858 + -1 Combine like terms: -1.825741858 + -1 = -2.825741858 X = -2.825741858 Simplifying X = -2.825741858Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.825741858, -2.825741858}
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