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Simplifying (x + 4)(x + 6) = 56 Reorder the terms: (4 + x)(x + 6) = 56 Reorder the terms: (4 + x)(6 + x) = 56 Multiply (4 + x) * (6 + x) (4(6 + x) + x(6 + x)) = 56 ((6 * 4 + x * 4) + x(6 + x)) = 56 ((24 + 4x) + x(6 + x)) = 56 (24 + 4x + (6 * x + x * x)) = 56 (24 + 4x + (6x + x2)) = 56 Combine like terms: 4x + 6x = 10x (24 + 10x + x2) = 56 Solving 24 + 10x + x2 = 56 Solving for variable 'x'. Reorder the terms: 24 + -56 + 10x + x2 = 56 + -56 Combine like terms: 24 + -56 = -32 -32 + 10x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -32 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 10x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 10x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 10x + x2 = 0 + 32 10x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 10x + x2 = 32 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 = 32 + 25 Reorder the terms: 25 + 10x + x2 = 32 + 25 Combine like terms: 32 + 25 = 57 25 + 10x + x2 = 57 Factor a perfect square on the left side: (x + 5)(x + 5) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 5) equal to 7.549834435 and -7.549834435.Subproblem 1
x + 5 = 7.549834435 Simplifying x + 5 = 7.549834435 Reorder the terms: 5 + x = 7.549834435 Solving 5 + x = 7.549834435 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 = 7.549834435 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.549834435 + -5 x = 7.549834435 + -5 Combine like terms: 7.549834435 + -5 = 2.549834435 x = 2.549834435 Simplifying x = 2.549834435Subproblem 2
x + 5 = -7.549834435 Simplifying x + 5 = -7.549834435 Reorder the terms: 5 + x = -7.549834435 Solving 5 + x = -7.549834435 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 = -7.549834435 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.549834435 + -5 x = -7.549834435 + -5 Combine like terms: -7.549834435 + -5 = -12.549834435 x = -12.549834435 Simplifying x = -12.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.549834435, -12.549834435}
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