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Simplifying x(x + 8) = 96 Reorder the terms: x(8 + x) = 96 (8 * x + x * x) = 96 (8x + x2) = 96 Solving 8x + x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 8x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 8x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 8x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 8x + x2 = 0 + 96 8x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 8x + x2 = 96 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 = 96 + 16 Reorder the terms: 16 + 8x + x2 = 96 + 16 Combine like terms: 96 + 16 = 112 16 + 8x + x2 = 112 Factor a perfect square on the left side: (x + 4)(x + 4) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + 4) equal to 10.583005244 and -10.583005244.Subproblem 1
x + 4 = 10.583005244 Simplifying x + 4 = 10.583005244 Reorder the terms: 4 + x = 10.583005244 Solving 4 + x = 10.583005244 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 = 10.583005244 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.583005244 + -4 x = 10.583005244 + -4 Combine like terms: 10.583005244 + -4 = 6.583005244 x = 6.583005244 Simplifying x = 6.583005244Subproblem 2
x + 4 = -10.583005244 Simplifying x + 4 = -10.583005244 Reorder the terms: 4 + x = -10.583005244 Solving 4 + x = -10.583005244 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 = -10.583005244 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.583005244 + -4 x = -10.583005244 + -4 Combine like terms: -10.583005244 + -4 = -14.583005244 x = -14.583005244 Simplifying x = -14.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.583005244, -14.583005244}
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