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Simplifying (x + 2)(x + 4) = 10000 Reorder the terms: (2 + x)(x + 4) = 10000 Reorder the terms: (2 + x)(4 + x) = 10000 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 10000 ((4 * 2 + x * 2) + x(4 + x)) = 10000 ((8 + 2x) + x(4 + x)) = 10000 (8 + 2x + (4 * x + x * x)) = 10000 (8 + 2x + (4x + x2)) = 10000 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 10000 Solving 8 + 6x + x2 = 10000 Solving for variable 'x'. Reorder the terms: 8 + -10000 + 6x + x2 = 10000 + -10000 Combine like terms: 8 + -10000 = -9992 -9992 + 6x + x2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 -9992 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9992' to each side of the equation. -9992 + 6x + 9992 + x2 = 0 + 9992 Reorder the terms: -9992 + 9992 + 6x + x2 = 0 + 9992 Combine like terms: -9992 + 9992 = 0 0 + 6x + x2 = 0 + 9992 6x + x2 = 0 + 9992 Combine like terms: 0 + 9992 = 9992 6x + x2 = 9992 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 = 9992 + 9 Reorder the terms: 9 + 6x + x2 = 9992 + 9 Combine like terms: 9992 + 9 = 10001 9 + 6x + x2 = 10001 Factor a perfect square on the left side: (x + 3)(x + 3) = 10001 Calculate the square root of the right side: 100.004999875 Break this problem into two subproblems by setting (x + 3) equal to 100.004999875 and -100.004999875.Subproblem 1
x + 3 = 100.004999875 Simplifying x + 3 = 100.004999875 Reorder the terms: 3 + x = 100.004999875 Solving 3 + x = 100.004999875 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 = 100.004999875 + -3 Combine like terms: 3 + -3 = 0 0 + x = 100.004999875 + -3 x = 100.004999875 + -3 Combine like terms: 100.004999875 + -3 = 97.004999875 x = 97.004999875 Simplifying x = 97.004999875Subproblem 2
x + 3 = -100.004999875 Simplifying x + 3 = -100.004999875 Reorder the terms: 3 + x = -100.004999875 Solving 3 + x = -100.004999875 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 = -100.004999875 + -3 Combine like terms: 3 + -3 = 0 0 + x = -100.004999875 + -3 x = -100.004999875 + -3 Combine like terms: -100.004999875 + -3 = -103.004999875 x = -103.004999875 Simplifying x = -103.004999875Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.004999875, -103.004999875}
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