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Simplifying (x + 6)(x + 4) = 6 Reorder the terms: (6 + x)(x + 4) = 6 Reorder the terms: (6 + x)(4 + x) = 6 Multiply (6 + x) * (4 + x) (6(4 + x) + x(4 + x)) = 6 ((4 * 6 + x * 6) + x(4 + x)) = 6 ((24 + 6x) + x(4 + x)) = 6 (24 + 6x + (4 * x + x * x)) = 6 (24 + 6x + (4x + x2)) = 6 Combine like terms: 6x + 4x = 10x (24 + 10x + x2) = 6 Solving 24 + 10x + x2 = 6 Solving for variable 'x'. Reorder the terms: 24 + -6 + 10x + x2 = 6 + -6 Combine like terms: 24 + -6 = 18 18 + 10x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 18 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 10x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 10x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 10x + x2 = 0 + -18 10x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 10x + x2 = -18 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 = -18 + 25 Reorder the terms: 25 + 10x + x2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + 10x + x2 = 7 Factor a perfect square on the left side: (x + 5)(x + 5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 5 = 2.645751311 Simplifying x + 5 = 2.645751311 Reorder the terms: 5 + x = 2.645751311 Solving 5 + x = 2.645751311 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 = 2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.645751311 + -5 x = 2.645751311 + -5 Combine like terms: 2.645751311 + -5 = -2.354248689 x = -2.354248689 Simplifying x = -2.354248689Subproblem 2
x + 5 = -2.645751311 Simplifying x + 5 = -2.645751311 Reorder the terms: 5 + x = -2.645751311 Solving 5 + x = -2.645751311 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 = -2.645751311 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.645751311 + -5 x = -2.645751311 + -5 Combine like terms: -2.645751311 + -5 = -7.645751311 x = -7.645751311 Simplifying x = -7.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.354248689, -7.645751311}
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