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Simplifying (X + 1)(X + 3) = 84 Reorder the terms: (1 + X)(X + 3) = 84 Reorder the terms: (1 + X)(3 + X) = 84 Multiply (1 + X) * (3 + X) (1(3 + X) + X(3 + X)) = 84 ((3 * 1 + X * 1) + X(3 + X)) = 84 ((3 + 1X) + X(3 + X)) = 84 (3 + 1X + (3 * X + X * X)) = 84 (3 + 1X + (3X + X2)) = 84 Combine like terms: 1X + 3X = 4X (3 + 4X + X2) = 84 Solving 3 + 4X + X2 = 84 Solving for variable 'X'. Reorder the terms: 3 + -84 + 4X + X2 = 84 + -84 Combine like terms: 3 + -84 = -81 -81 + 4X + X2 = 84 + -84 Combine like terms: 84 + -84 = 0 -81 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 4X + 81 + X2 = 0 + 81 Reorder the terms: -81 + 81 + 4X + X2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 4X + X2 = 0 + 81 4X + X2 = 0 + 81 Combine like terms: 0 + 81 = 81 4X + X2 = 81 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 81 + 4 Reorder the terms: 4 + 4X + X2 = 81 + 4 Combine like terms: 81 + 4 = 85 4 + 4X + X2 = 85 Factor a perfect square on the left side: (X + 2)(X + 2) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (X + 2) equal to 9.219544457 and -9.219544457.Subproblem 1
X + 2 = 9.219544457 Simplifying X + 2 = 9.219544457 Reorder the terms: 2 + X = 9.219544457 Solving 2 + X = 9.219544457 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 9.219544457 + -2 Combine like terms: 2 + -2 = 0 0 + X = 9.219544457 + -2 X = 9.219544457 + -2 Combine like terms: 9.219544457 + -2 = 7.219544457 X = 7.219544457 Simplifying X = 7.219544457Subproblem 2
X + 2 = -9.219544457 Simplifying X + 2 = -9.219544457 Reorder the terms: 2 + X = -9.219544457 Solving 2 + X = -9.219544457 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -9.219544457 + -2 Combine like terms: 2 + -2 = 0 0 + X = -9.219544457 + -2 X = -9.219544457 + -2 Combine like terms: -9.219544457 + -2 = -11.219544457 X = -11.219544457 Simplifying X = -11.219544457Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.219544457, -11.219544457}
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