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Simplifying (x + -1)(x + 1) + 3 + -2x = 3x + (x + -1) * 3 Reorder the terms: (-1 + x)(x + 1) + 3 + -2x = 3x + (x + -1) * 3 Reorder the terms: (-1 + x)(1 + x) + 3 + -2x = 3x + (x + -1) * 3 Multiply (-1 + x) * (1 + x) (-1(1 + x) + x(1 + x)) + 3 + -2x = 3x + (x + -1) * 3 ((1 * -1 + x * -1) + x(1 + x)) + 3 + -2x = 3x + (x + -1) * 3 ((-1 + -1x) + x(1 + x)) + 3 + -2x = 3x + (x + -1) * 3 (-1 + -1x + (1 * x + x * x)) + 3 + -2x = 3x + (x + -1) * 3 (-1 + -1x + (1x + x2)) + 3 + -2x = 3x + (x + -1) * 3 Combine like terms: -1x + 1x = 0 (-1 + 0 + x2) + 3 + -2x = 3x + (x + -1) * 3 (-1 + x2) + 3 + -2x = 3x + (x + -1) * 3 Reorder the terms: -1 + 3 + -2x + x2 = 3x + (x + -1) * 3 Combine like terms: -1 + 3 = 2 2 + -2x + x2 = 3x + (x + -1) * 3 Reorder the terms: 2 + -2x + x2 = 3x + (-1 + x) * 3 Reorder the terms for easier multiplication: 2 + -2x + x2 = 3x + 3(-1 + x) 2 + -2x + x2 = 3x + (-1 * 3 + x * 3) 2 + -2x + x2 = 3x + (-3 + 3x) Reorder the terms: 2 + -2x + x2 = -3 + 3x + 3x Combine like terms: 3x + 3x = 6x 2 + -2x + x2 = -3 + 6x Solving 2 + -2x + x2 = -3 + 6x Solving for variable 'x'. Reorder the terms: 2 + 3 + -2x + -6x + x2 = -3 + 6x + 3 + -6x Combine like terms: 2 + 3 = 5 5 + -2x + -6x + x2 = -3 + 6x + 3 + -6x Combine like terms: -2x + -6x = -8x 5 + -8x + x2 = -3 + 6x + 3 + -6x Reorder the terms: 5 + -8x + x2 = -3 + 3 + 6x + -6x Combine like terms: -3 + 3 = 0 5 + -8x + x2 = 0 + 6x + -6x 5 + -8x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 5 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -8x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x + x2 = 0 + -5 -8x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8x + x2 = -5 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 = -5 + 16 Reorder the terms: 16 + -8x + x2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8x + x2 = 11 Factor a perfect square on the left side: (x + -4)(x + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -4 = 3.31662479 Simplifying x + -4 = 3.31662479 Reorder the terms: -4 + x = 3.31662479 Solving -4 + x = 3.31662479 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 = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.31662479 + 4 x = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 x = 7.31662479 Simplifying x = 7.31662479Subproblem 2
x + -4 = -3.31662479 Simplifying x + -4 = -3.31662479 Reorder the terms: -4 + x = -3.31662479 Solving -4 + x = -3.31662479 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 = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.31662479 + 4 x = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 x = 0.68337521 Simplifying x = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.31662479, 0.68337521}
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