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Simplifying (x + -3)(x + -2) = 7x + -1 Reorder the terms: (-3 + x)(x + -2) = 7x + -1 Reorder the terms: (-3 + x)(-2 + x) = 7x + -1 Multiply (-3 + x) * (-2 + x) (-3(-2 + x) + x(-2 + x)) = 7x + -1 ((-2 * -3 + x * -3) + x(-2 + x)) = 7x + -1 ((6 + -3x) + x(-2 + x)) = 7x + -1 (6 + -3x + (-2 * x + x * x)) = 7x + -1 (6 + -3x + (-2x + x2)) = 7x + -1 Combine like terms: -3x + -2x = -5x (6 + -5x + x2) = 7x + -1 Reorder the terms: 6 + -5x + x2 = -1 + 7x Solving 6 + -5x + x2 = -1 + 7x Solving for variable 'x'. Reorder the terms: 6 + 1 + -5x + -7x + x2 = -1 + 7x + 1 + -7x Combine like terms: 6 + 1 = 7 7 + -5x + -7x + x2 = -1 + 7x + 1 + -7x Combine like terms: -5x + -7x = -12x 7 + -12x + x2 = -1 + 7x + 1 + -7x Reorder the terms: 7 + -12x + x2 = -1 + 1 + 7x + -7x Combine like terms: -1 + 1 = 0 7 + -12x + x2 = 0 + 7x + -7x 7 + -12x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 7 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -12x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -12x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -12x + x2 = 0 + -7 -12x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -12x + x2 = -7 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -7 + 36 Reorder the terms: 36 + -12x + x2 = -7 + 36 Combine like terms: -7 + 36 = 29 36 + -12x + x2 = 29 Factor a perfect square on the left side: (x + -6)(x + -6) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -6) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -6 = 5.385164807 Simplifying x + -6 = 5.385164807 Reorder the terms: -6 + x = 5.385164807 Solving -6 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.385164807 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.385164807 + 6 x = 5.385164807 + 6 Combine like terms: 5.385164807 + 6 = 11.385164807 x = 11.385164807 Simplifying x = 11.385164807Subproblem 2
x + -6 = -5.385164807 Simplifying x + -6 = -5.385164807 Reorder the terms: -6 + x = -5.385164807 Solving -6 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.385164807 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.385164807 + 6 x = -5.385164807 + 6 Combine like terms: -5.385164807 + 6 = 0.614835193 x = 0.614835193 Simplifying x = 0.614835193Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.385164807, 0.614835193}
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