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Simplifying (x + 2)(x + 4) = 100 Reorder the terms: (2 + x)(x + 4) = 100 Reorder the terms: (2 + x)(4 + x) = 100 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 100 ((4 * 2 + x * 2) + x(4 + x)) = 100 ((8 + 2x) + x(4 + x)) = 100 (8 + 2x + (4 * x + x * x)) = 100 (8 + 2x + (4x + x2)) = 100 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 100 Solving 8 + 6x + x2 = 100 Solving for variable 'x'. Reorder the terms: 8 + -100 + 6x + x2 = 100 + -100 Combine like terms: 8 + -100 = -92 -92 + 6x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -92 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 6x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 6x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 6x + x2 = 0 + 92 6x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 6x + x2 = 92 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 = 92 + 9 Reorder the terms: 9 + 6x + x2 = 92 + 9 Combine like terms: 92 + 9 = 101 9 + 6x + x2 = 101 Factor a perfect square on the left side: (x + 3)(x + 3) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 3) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 3 = 10.049875621 Simplifying x + 3 = 10.049875621 Reorder the terms: 3 + x = 10.049875621 Solving 3 + x = 10.049875621 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 = 10.049875621 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.049875621 + -3 x = 10.049875621 + -3 Combine like terms: 10.049875621 + -3 = 7.049875621 x = 7.049875621 Simplifying x = 7.049875621Subproblem 2
x + 3 = -10.049875621 Simplifying x + 3 = -10.049875621 Reorder the terms: 3 + x = -10.049875621 Solving 3 + x = -10.049875621 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 = -10.049875621 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.049875621 + -3 x = -10.049875621 + -3 Combine like terms: -10.049875621 + -3 = -13.049875621 x = -13.049875621 Simplifying x = -13.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.049875621, -13.049875621}
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