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Simplifying (x + -1)(x + 1) + 15 = 8x Reorder the terms: (-1 + x)(x + 1) + 15 = 8x Reorder the terms: (-1 + x)(1 + x) + 15 = 8x Multiply (-1 + x) * (1 + x) (-1(1 + x) + x(1 + x)) + 15 = 8x ((1 * -1 + x * -1) + x(1 + x)) + 15 = 8x ((-1 + -1x) + x(1 + x)) + 15 = 8x (-1 + -1x + (1 * x + x * x)) + 15 = 8x (-1 + -1x + (1x + x2)) + 15 = 8x Combine like terms: -1x + 1x = 0 (-1 + 0 + x2) + 15 = 8x (-1 + x2) + 15 = 8x Reorder the terms: -1 + 15 + x2 = 8x Combine like terms: -1 + 15 = 14 14 + x2 = 8x Solving 14 + x2 = 8x Solving for variable 'x'. Reorder the terms: 14 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 14 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -8x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8x + x2 = 0 + -14 -8x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8x + x2 = -14 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 = -14 + 16 Reorder the terms: 16 + -8x + x2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8x + x2 = 2 Factor a perfect square on the left side: (x + -4)(x + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -4 = 1.414213562 Simplifying x + -4 = 1.414213562 Reorder the terms: -4 + x = 1.414213562 Solving -4 + x = 1.414213562 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 = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.414213562 + 4 x = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 x = 5.414213562 Simplifying x = 5.414213562Subproblem 2
x + -4 = -1.414213562 Simplifying x + -4 = -1.414213562 Reorder the terms: -4 + x = -1.414213562 Solving -4 + x = -1.414213562 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 = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.414213562 + 4 x = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 x = 2.585786438 Simplifying x = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.414213562, 2.585786438}
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