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Simplifying (x + -1)(x + 1) + 8 = 6x Reorder the terms: (-1 + x)(x + 1) + 8 = 6x Reorder the terms: (-1 + x)(1 + x) + 8 = 6x Multiply (-1 + x) * (1 + x) (-1(1 + x) + x(1 + x)) + 8 = 6x ((1 * -1 + x * -1) + x(1 + x)) + 8 = 6x ((-1 + -1x) + x(1 + x)) + 8 = 6x (-1 + -1x + (1 * x + x * x)) + 8 = 6x (-1 + -1x + (1x + x2)) + 8 = 6x Combine like terms: -1x + 1x = 0 (-1 + 0 + x2) + 8 = 6x (-1 + x2) + 8 = 6x Reorder the terms: -1 + 8 + x2 = 6x Combine like terms: -1 + 8 = 7 7 + x2 = 6x Solving 7 + x2 = 6x Solving for variable 'x'. Reorder the terms: 7 + -6x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 7 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -6x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x + x2 = 0 + -7 -6x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6x + x2 = -7 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7 + 9 Reorder the terms: 9 + -6x + x2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6x + x2 = 2 Factor a perfect square on the left side: (x + -3)(x + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -3 = 1.414213562 Simplifying x + -3 = 1.414213562 Reorder the terms: -3 + x = 1.414213562 Solving -3 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.414213562 + 3 x = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 x = 4.414213562 Simplifying x = 4.414213562Subproblem 2
x + -3 = -1.414213562 Simplifying x + -3 = -1.414213562 Reorder the terms: -3 + x = -1.414213562 Solving -3 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.414213562 + 3 x = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 x = 1.585786438 Simplifying x = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.414213562, 1.585786438}
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