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Simplifying (x + 7)(x + -1) = (2x + 1) Reorder the terms: (7 + x)(x + -1) = (2x + 1) Reorder the terms: (7 + x)(-1 + x) = (2x + 1) Multiply (7 + x) * (-1 + x) (7(-1 + x) + x(-1 + x)) = (2x + 1) ((-1 * 7 + x * 7) + x(-1 + x)) = (2x + 1) ((-7 + 7x) + x(-1 + x)) = (2x + 1) (-7 + 7x + (-1 * x + x * x)) = (2x + 1) (-7 + 7x + (-1x + x2)) = (2x + 1) Combine like terms: 7x + -1x = 6x (-7 + 6x + x2) = (2x + 1) Reorder the terms: -7 + 6x + x2 = (1 + 2x) Remove parenthesis around (1 + 2x) -7 + 6x + x2 = 1 + 2x Solving -7 + 6x + x2 = 1 + 2x Solving for variable 'x'. Reorder the terms: -7 + -1 + 6x + -2x + x2 = 1 + 2x + -1 + -2x Combine like terms: -7 + -1 = -8 -8 + 6x + -2x + x2 = 1 + 2x + -1 + -2x Combine like terms: 6x + -2x = 4x -8 + 4x + x2 = 1 + 2x + -1 + -2x Reorder the terms: -8 + 4x + x2 = 1 + -1 + 2x + -2x Combine like terms: 1 + -1 = 0 -8 + 4x + x2 = 0 + 2x + -2x -8 + 4x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -8 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 4x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 4x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4x + x2 = 0 + 8 4x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 4x + x2 = 8 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 8 + 4 Reorder the terms: 4 + 4x + x2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4x + x2 = 12 Factor a perfect square on the left side: (x + 2)(x + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
x + 2 = 3.464101615 Simplifying x + 2 = 3.464101615 Reorder the terms: 2 + x = 3.464101615 Solving 2 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.464101615 + -2 x = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 x = 1.464101615 Simplifying x = 1.464101615Subproblem 2
x + 2 = -3.464101615 Simplifying x + 2 = -3.464101615 Reorder the terms: 2 + x = -3.464101615 Solving 2 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.464101615 + -2 x = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 x = -5.464101615 Simplifying x = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.464101615, -5.464101615}
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