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Simplifying 2(x + 2) * 2(2x + 4) = 43.2 Reorder the terms: 2(2 + x) * 2(2x + 4) = 43.2 Reorder the terms: 2(2 + x) * 2(4 + 2x) = 43.2 Reorder the terms for easier multiplication: 2 * 2(2 + x)(4 + 2x) = 43.2 Multiply 2 * 2 4(2 + x)(4 + 2x) = 43.2 Multiply (2 + x) * (4 + 2x) 4(2(4 + 2x) + x(4 + 2x)) = 43.2 4((4 * 2 + 2x * 2) + x(4 + 2x)) = 43.2 4((8 + 4x) + x(4 + 2x)) = 43.2 4(8 + 4x + (4 * x + 2x * x)) = 43.2 4(8 + 4x + (4x + 2x2)) = 43.2 Combine like terms: 4x + 4x = 8x 4(8 + 8x + 2x2) = 43.2 (8 * 4 + 8x * 4 + 2x2 * 4) = 43.2 (32 + 32x + 8x2) = 43.2 Solving 32 + 32x + 8x2 = 43.2 Solving for variable 'x'. Reorder the terms: 32 + -43.2 + 32x + 8x2 = 43.2 + -43.2 Combine like terms: 32 + -43.2 = -11.2 -11.2 + 32x + 8x2 = 43.2 + -43.2 Combine like terms: 43.2 + -43.2 = 0.0 -11.2 + 32x + 8x2 = 0.0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.4 + 4x + x2 = 0.0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 4x + 1.4 + x2 = 0.0 + 1.4 Reorder the terms: -1.4 + 1.4 + 4x + x2 = 0.0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 4x + x2 = 0.0 + 1.4 4x + x2 = 0.0 + 1.4 Combine like terms: 0.0 + 1.4 = 1.4 4x + x2 = 1.4 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 = 1.4 + 4 Reorder the terms: 4 + 4x + x2 = 1.4 + 4 Combine like terms: 1.4 + 4 = 5.4 4 + 4x + x2 = 5.4 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.4 Calculate the square root of the right side: 2.323790008 Break this problem into two subproblems by setting (x + 2) equal to 2.323790008 and -2.323790008.Subproblem 1
x + 2 = 2.323790008 Simplifying x + 2 = 2.323790008 Reorder the terms: 2 + x = 2.323790008 Solving 2 + x = 2.323790008 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 = 2.323790008 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.323790008 + -2 x = 2.323790008 + -2 Combine like terms: 2.323790008 + -2 = 0.323790008 x = 0.323790008 Simplifying x = 0.323790008Subproblem 2
x + 2 = -2.323790008 Simplifying x + 2 = -2.323790008 Reorder the terms: 2 + x = -2.323790008 Solving 2 + x = -2.323790008 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 = -2.323790008 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.323790008 + -2 x = -2.323790008 + -2 Combine like terms: -2.323790008 + -2 = -4.323790008 x = -4.323790008 Simplifying x = -4.323790008Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.323790008, -4.323790008}
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