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Simplifying 8x(x + 8) = x + 36 Reorder the terms: 8x(8 + x) = x + 36 (8 * 8x + x * 8x) = x + 36 (64x + 8x2) = x + 36 Reorder the terms: 64x + 8x2 = 36 + x Solving 64x + 8x2 = 36 + x Solving for variable 'x'. Reorder the terms: -36 + 64x + -1x + 8x2 = 36 + x + -36 + -1x Combine like terms: 64x + -1x = 63x -36 + 63x + 8x2 = 36 + x + -36 + -1x Reorder the terms: -36 + 63x + 8x2 = 36 + -36 + x + -1x Combine like terms: 36 + -36 = 0 -36 + 63x + 8x2 = 0 + x + -1x -36 + 63x + 8x2 = x + -1x Combine like terms: x + -1x = 0 -36 + 63x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.5 + 7.875x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 7.875x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 7.875x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 7.875x + x2 = 0 + 4.5 7.875x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 7.875x + x2 = 4.5 The x term is 7.875x. Take half its coefficient (3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. 7.875x + 15.50390625 + x2 = 4.5 + 15.50390625 Reorder the terms: 15.50390625 + 7.875x + x2 = 4.5 + 15.50390625 Combine like terms: 4.5 + 15.50390625 = 20.00390625 15.50390625 + 7.875x + x2 = 20.00390625 Factor a perfect square on the left side: (x + 3.9375)(x + 3.9375) = 20.00390625 Calculate the square root of the right side: 4.472572666 Break this problem into two subproblems by setting (x + 3.9375) equal to 4.472572666 and -4.472572666.Subproblem 1
x + 3.9375 = 4.472572666 Simplifying x + 3.9375 = 4.472572666 Reorder the terms: 3.9375 + x = 4.472572666 Solving 3.9375 + x = 4.472572666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + x = 4.472572666 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + x = 4.472572666 + -3.9375 x = 4.472572666 + -3.9375 Combine like terms: 4.472572666 + -3.9375 = 0.535072666 x = 0.535072666 Simplifying x = 0.535072666Subproblem 2
x + 3.9375 = -4.472572666 Simplifying x + 3.9375 = -4.472572666 Reorder the terms: 3.9375 + x = -4.472572666 Solving 3.9375 + x = -4.472572666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + x = -4.472572666 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + x = -4.472572666 + -3.9375 x = -4.472572666 + -3.9375 Combine like terms: -4.472572666 + -3.9375 = -8.410072666 x = -8.410072666 Simplifying x = -8.410072666Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.535072666, -8.410072666}
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