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Simplifying (x + 4)(x + 2) = 55 Reorder the terms: (4 + x)(x + 2) = 55 Reorder the terms: (4 + x)(2 + x) = 55 Multiply (4 + x) * (2 + x) (4(2 + x) + x(2 + x)) = 55 ((2 * 4 + x * 4) + x(2 + x)) = 55 ((8 + 4x) + x(2 + x)) = 55 (8 + 4x + (2 * x + x * x)) = 55 (8 + 4x + (2x + x2)) = 55 Combine like terms: 4x + 2x = 6x (8 + 6x + x2) = 55 Solving 8 + 6x + x2 = 55 Solving for variable 'x'. Reorder the terms: 8 + -55 + 6x + x2 = 55 + -55 Combine like terms: 8 + -55 = -47 -47 + 6x + x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -47 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 6x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 6x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 6x + x2 = 0 + 47 6x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 6x + x2 = 47 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 47 + 9 Reorder the terms: 9 + 6x + x2 = 47 + 9 Combine like terms: 47 + 9 = 56 9 + 6x + x2 = 56 Factor a perfect square on the left side: (x + 3)(x + 3) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 3) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 3 = 7.483314774 Simplifying x + 3 = 7.483314774 Reorder the terms: 3 + x = 7.483314774 Solving 3 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.483314774 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.483314774 + -3 x = 7.483314774 + -3 Combine like terms: 7.483314774 + -3 = 4.483314774 x = 4.483314774 Simplifying x = 4.483314774Subproblem 2
x + 3 = -7.483314774 Simplifying x + 3 = -7.483314774 Reorder the terms: 3 + x = -7.483314774 Solving 3 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.483314774 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.483314774 + -3 x = -7.483314774 + -3 Combine like terms: -7.483314774 + -3 = -10.483314774 x = -10.483314774 Simplifying x = -10.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.483314774, -10.483314774}
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