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Simplifying 2x(4x + 8) = 11 + -1(x + 2) Reorder the terms: 2x(8 + 4x) = 11 + -1(x + 2) (8 * 2x + 4x * 2x) = 11 + -1(x + 2) (16x + 8x2) = 11 + -1(x + 2) Reorder the terms: 16x + 8x2 = 11 + -1(2 + x) 16x + 8x2 = 11 + (2 * -1 + x * -1) 16x + 8x2 = 11 + (-2 + -1x) Combine like terms: 11 + -2 = 9 16x + 8x2 = 9 + -1x Solving 16x + 8x2 = 9 + -1x Solving for variable 'x'. Reorder the terms: -9 + 16x + x + 8x2 = 9 + -1x + -9 + x Combine like terms: 16x + x = 17x -9 + 17x + 8x2 = 9 + -1x + -9 + x Reorder the terms: -9 + 17x + 8x2 = 9 + -9 + -1x + x Combine like terms: 9 + -9 = 0 -9 + 17x + 8x2 = 0 + -1x + x -9 + 17x + 8x2 = -1x + x Combine like terms: -1x + x = 0 -9 + 17x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 2.125x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 2.125x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 2.125x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 2.125x + x2 = 0 + 1.125 2.125x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 2.125x + x2 = 1.125 The x term is 2.125x. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125x + 1.12890625 + x2 = 1.125 + 1.12890625 Reorder the terms: 1.12890625 + 2.125x + x2 = 1.125 + 1.12890625 Combine like terms: 1.125 + 1.12890625 = 2.25390625 1.12890625 + 2.125x + x2 = 2.25390625 Factor a perfect square on the left side: (x + 1.0625)(x + 1.0625) = 2.25390625 Calculate the square root of the right side: 1.501301519 Break this problem into two subproblems by setting (x + 1.0625) equal to 1.501301519 and -1.501301519.Subproblem 1
x + 1.0625 = 1.501301519 Simplifying x + 1.0625 = 1.501301519 Reorder the terms: 1.0625 + x = 1.501301519 Solving 1.0625 + x = 1.501301519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = 1.501301519 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = 1.501301519 + -1.0625 x = 1.501301519 + -1.0625 Combine like terms: 1.501301519 + -1.0625 = 0.438801519 x = 0.438801519 Simplifying x = 0.438801519Subproblem 2
x + 1.0625 = -1.501301519 Simplifying x + 1.0625 = -1.501301519 Reorder the terms: 1.0625 + x = -1.501301519 Solving 1.0625 + x = -1.501301519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + x = -1.501301519 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + x = -1.501301519 + -1.0625 x = -1.501301519 + -1.0625 Combine like terms: -1.501301519 + -1.0625 = -2.563801519 x = -2.563801519 Simplifying x = -2.563801519Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.438801519, -2.563801519}
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