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Simplifying (2 + x)(2 + 2x) = 551 Multiply (2 + x) * (2 + 2x) (2(2 + 2x) + x(2 + 2x)) = 551 ((2 * 2 + 2x * 2) + x(2 + 2x)) = 551 ((4 + 4x) + x(2 + 2x)) = 551 (4 + 4x + (2 * x + 2x * x)) = 551 (4 + 4x + (2x + 2x2)) = 551 Combine like terms: 4x + 2x = 6x (4 + 6x + 2x2) = 551 Solving 4 + 6x + 2x2 = 551 Solving for variable 'x'. Reorder the terms: 4 + -551 + 6x + 2x2 = 551 + -551 Combine like terms: 4 + -551 = -547 -547 + 6x + 2x2 = 551 + -551 Combine like terms: 551 + -551 = 0 -547 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -273.5 + 3x + x2 = 0 Move the constant term to the right: Add '273.5' to each side of the equation. -273.5 + 3x + 273.5 + x2 = 0 + 273.5 Reorder the terms: -273.5 + 273.5 + 3x + x2 = 0 + 273.5 Combine like terms: -273.5 + 273.5 = 0.0 0.0 + 3x + x2 = 0 + 273.5 3x + x2 = 0 + 273.5 Combine like terms: 0 + 273.5 = 273.5 3x + x2 = 273.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 273.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 273.5 + 2.25 Combine like terms: 273.5 + 2.25 = 275.75 2.25 + 3x + x2 = 275.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 275.75 Calculate the square root of the right side: 16.605721905 Break this problem into two subproblems by setting (x + 1.5) equal to 16.605721905 and -16.605721905.Subproblem 1
x + 1.5 = 16.605721905 Simplifying x + 1.5 = 16.605721905 Reorder the terms: 1.5 + x = 16.605721905 Solving 1.5 + x = 16.605721905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 16.605721905 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 16.605721905 + -1.5 x = 16.605721905 + -1.5 Combine like terms: 16.605721905 + -1.5 = 15.105721905 x = 15.105721905 Simplifying x = 15.105721905Subproblem 2
x + 1.5 = -16.605721905 Simplifying x + 1.5 = -16.605721905 Reorder the terms: 1.5 + x = -16.605721905 Solving 1.5 + x = -16.605721905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -16.605721905 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -16.605721905 + -1.5 x = -16.605721905 + -1.5 Combine like terms: -16.605721905 + -1.5 = -18.105721905 x = -18.105721905 Simplifying x = -18.105721905Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.105721905, -18.105721905}
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