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Simplifying x(x + 8) = 6336 Reorder the terms: x(8 + x) = 6336 (8 * x + x * x) = 6336 (8x + x2) = 6336 Solving 8x + x2 = 6336 Solving for variable 'x'. Reorder the terms: -6336 + 8x + x2 = 6336 + -6336 Combine like terms: 6336 + -6336 = 0 -6336 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6336' to each side of the equation. -6336 + 8x + 6336 + x2 = 0 + 6336 Reorder the terms: -6336 + 6336 + 8x + x2 = 0 + 6336 Combine like terms: -6336 + 6336 = 0 0 + 8x + x2 = 0 + 6336 8x + x2 = 0 + 6336 Combine like terms: 0 + 6336 = 6336 8x + x2 = 6336 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 = 6336 + 16 Reorder the terms: 16 + 8x + x2 = 6336 + 16 Combine like terms: 6336 + 16 = 6352 16 + 8x + x2 = 6352 Factor a perfect square on the left side: (x + 4)(x + 4) = 6352 Calculate the square root of the right side: 79.699435381 Break this problem into two subproblems by setting (x + 4) equal to 79.699435381 and -79.699435381.Subproblem 1
x + 4 = 79.699435381 Simplifying x + 4 = 79.699435381 Reorder the terms: 4 + x = 79.699435381 Solving 4 + x = 79.699435381 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 = 79.699435381 + -4 Combine like terms: 4 + -4 = 0 0 + x = 79.699435381 + -4 x = 79.699435381 + -4 Combine like terms: 79.699435381 + -4 = 75.699435381 x = 75.699435381 Simplifying x = 75.699435381Subproblem 2
x + 4 = -79.699435381 Simplifying x + 4 = -79.699435381 Reorder the terms: 4 + x = -79.699435381 Solving 4 + x = -79.699435381 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 = -79.699435381 + -4 Combine like terms: 4 + -4 = 0 0 + x = -79.699435381 + -4 x = -79.699435381 + -4 Combine like terms: -79.699435381 + -4 = -83.699435381 x = -83.699435381 Simplifying x = -83.699435381Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.699435381, -83.699435381}
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