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Simplifying x(x + 8) + (x + 16) = 888 Reorder the terms: x(8 + x) + (x + 16) = 888 (8 * x + x * x) + (x + 16) = 888 (8x + x2) + (x + 16) = 888 Reorder the terms: 8x + x2 + (16 + x) = 888 Remove parenthesis around (16 + x) 8x + x2 + 16 + x = 888 Reorder the terms: 16 + 8x + x + x2 = 888 Combine like terms: 8x + x = 9x 16 + 9x + x2 = 888 Solving 16 + 9x + x2 = 888 Solving for variable 'x'. Reorder the terms: 16 + -888 + 9x + x2 = 888 + -888 Combine like terms: 16 + -888 = -872 -872 + 9x + x2 = 888 + -888 Combine like terms: 888 + -888 = 0 -872 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '872' to each side of the equation. -872 + 9x + 872 + x2 = 0 + 872 Reorder the terms: -872 + 872 + 9x + x2 = 0 + 872 Combine like terms: -872 + 872 = 0 0 + 9x + x2 = 0 + 872 9x + x2 = 0 + 872 Combine like terms: 0 + 872 = 872 9x + x2 = 872 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 872 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 872 + 20.25 Combine like terms: 872 + 20.25 = 892.25 20.25 + 9x + x2 = 892.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 892.25 Calculate the square root of the right side: 29.870554062 Break this problem into two subproblems by setting (x + 4.5) equal to 29.870554062 and -29.870554062.Subproblem 1
x + 4.5 = 29.870554062 Simplifying x + 4.5 = 29.870554062 Reorder the terms: 4.5 + x = 29.870554062 Solving 4.5 + x = 29.870554062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 29.870554062 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 29.870554062 + -4.5 x = 29.870554062 + -4.5 Combine like terms: 29.870554062 + -4.5 = 25.370554062 x = 25.370554062 Simplifying x = 25.370554062Subproblem 2
x + 4.5 = -29.870554062 Simplifying x + 4.5 = -29.870554062 Reorder the terms: 4.5 + x = -29.870554062 Solving 4.5 + x = -29.870554062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -29.870554062 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -29.870554062 + -4.5 x = -29.870554062 + -4.5 Combine like terms: -29.870554062 + -4.5 = -34.370554062 x = -34.370554062 Simplifying x = -34.370554062Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.370554062, -34.370554062}
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