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Simplifying (x + 1)(x + 4)(1) = 84 Reorder the terms: (1 + x)(x + 4)(1) = 84 Reorder the terms: (1 + x)(4 + x)(1) = 84 Reorder the terms for easier multiplication: 1(1 + x)(4 + x) = 84 Multiply (1 + x) * (4 + x) 1(1(4 + x) + x(4 + x)) = 84 1((4 * 1 + x * 1) + x(4 + x)) = 84 1((4 + 1x) + x(4 + x)) = 84 1(4 + 1x + (4 * x + x * x)) = 84 1(4 + 1x + (4x + x2)) = 84 Combine like terms: 1x + 4x = 5x 1(4 + 5x + x2) = 84 (4 * 1 + 5x * 1 + x2 * 1) = 84 (4 + 5x + 1x2) = 84 Solving 4 + 5x + 1x2 = 84 Solving for variable 'x'. Reorder the terms: 4 + -84 + 5x + 1x2 = 84 + -84 Combine like terms: 4 + -84 = -80 -80 + 5x + 1x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -80 + 5x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 5x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 5x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 5x + x2 = 0 + 80 5x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 5x + x2 = 80 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 80 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 80 + 6.25 Combine like terms: 80 + 6.25 = 86.25 6.25 + 5x + x2 = 86.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + 2.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + 2.5 = 9.287087811 Simplifying x + 2.5 = 9.287087811 Reorder the terms: 2.5 + x = 9.287087811 Solving 2.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 9.287087811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.287087811 + -2.5 x = 9.287087811 + -2.5 Combine like terms: 9.287087811 + -2.5 = 6.787087811 x = 6.787087811 Simplifying x = 6.787087811Subproblem 2
x + 2.5 = -9.287087811 Simplifying x + 2.5 = -9.287087811 Reorder the terms: 2.5 + x = -9.287087811 Solving 2.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -9.287087811 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.287087811 + -2.5 x = -9.287087811 + -2.5 Combine like terms: -9.287087811 + -2.5 = -11.787087811 x = -11.787087811 Simplifying x = -11.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.787087811, -11.787087811}
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