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Simplifying (x + 6)(x + 4) = 22 Reorder the terms: (6 + x)(x + 4) = 22 Reorder the terms: (6 + x)(4 + x) = 22 Multiply (6 + x) * (4 + x) (6(4 + x) + x(4 + x)) = 22 ((4 * 6 + x * 6) + x(4 + x)) = 22 ((24 + 6x) + x(4 + x)) = 22 (24 + 6x + (4 * x + x * x)) = 22 (24 + 6x + (4x + x2)) = 22 Combine like terms: 6x + 4x = 10x (24 + 10x + x2) = 22 Solving 24 + 10x + x2 = 22 Solving for variable 'x'. Reorder the terms: 24 + -22 + 10x + x2 = 22 + -22 Combine like terms: 24 + -22 = 2 2 + 10x + x2 = 22 + -22 Combine like terms: 22 + -22 = 0 2 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 10x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 10x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 10x + x2 = 0 + -2 10x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 10x + x2 = -2 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -2 + 25 Reorder the terms: 25 + 10x + x2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + 10x + x2 = 23 Factor a perfect square on the left side: (x + 5)(x + 5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 5) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 5 = 4.795831523 Simplifying x + 5 = 4.795831523 Reorder the terms: 5 + x = 4.795831523 Solving 5 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.795831523 + -5 x = 4.795831523 + -5 Combine like terms: 4.795831523 + -5 = -0.204168477 x = -0.204168477 Simplifying x = -0.204168477Subproblem 2
x + 5 = -4.795831523 Simplifying x + 5 = -4.795831523 Reorder the terms: 5 + x = -4.795831523 Solving 5 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.795831523 + -5 x = -4.795831523 + -5 Combine like terms: -4.795831523 + -5 = -9.795831523 x = -9.795831523 Simplifying x = -9.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.204168477, -9.795831523}
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