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Simplifying x(x + 8) = 2504 Reorder the terms: x(8 + x) = 2504 (8 * x + x * x) = 2504 (8x + x2) = 2504 Solving 8x + x2 = 2504 Solving for variable 'x'. Reorder the terms: -2504 + 8x + x2 = 2504 + -2504 Combine like terms: 2504 + -2504 = 0 -2504 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2504' to each side of the equation. -2504 + 8x + 2504 + x2 = 0 + 2504 Reorder the terms: -2504 + 2504 + 8x + x2 = 0 + 2504 Combine like terms: -2504 + 2504 = 0 0 + 8x + x2 = 0 + 2504 8x + x2 = 0 + 2504 Combine like terms: 0 + 2504 = 2504 8x + x2 = 2504 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 2504 + 16 Reorder the terms: 16 + 8x + x2 = 2504 + 16 Combine like terms: 2504 + 16 = 2520 16 + 8x + x2 = 2520 Factor a perfect square on the left side: (x + 4)(x + 4) = 2520 Calculate the square root of the right side: 50.199601592 Break this problem into two subproblems by setting (x + 4) equal to 50.199601592 and -50.199601592.Subproblem 1
x + 4 = 50.199601592 Simplifying x + 4 = 50.199601592 Reorder the terms: 4 + x = 50.199601592 Solving 4 + x = 50.199601592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 50.199601592 + -4 Combine like terms: 4 + -4 = 0 0 + x = 50.199601592 + -4 x = 50.199601592 + -4 Combine like terms: 50.199601592 + -4 = 46.199601592 x = 46.199601592 Simplifying x = 46.199601592Subproblem 2
x + 4 = -50.199601592 Simplifying x + 4 = -50.199601592 Reorder the terms: 4 + x = -50.199601592 Solving 4 + x = -50.199601592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -50.199601592 + -4 Combine like terms: 4 + -4 = 0 0 + x = -50.199601592 + -4 x = -50.199601592 + -4 Combine like terms: -50.199601592 + -4 = -54.199601592 x = -54.199601592 Simplifying x = -54.199601592Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.199601592, -54.199601592}
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