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Simplifying (x + 7) * 2 + -1(x + (-2))(x + (-1)) = 0 Reorder the terms: (7 + x) * 2 + -1(x + (-2))(x + (-1)) = 0 Reorder the terms for easier multiplication: 2(7 + x) + -1(x + (-2))(x + (-1)) = 0 (7 * 2 + x * 2) + -1(x + (-2))(x + (-1)) = 0 (14 + 2x) + -1(x + (-2))(x + (-1)) = 0 14 + 2x + -1(x + -2)(x + (-1)) = 0 Reorder the terms: 14 + 2x + -1(-2 + x)(x + (-1)) = 0 14 + 2x + -1(-2 + x)(x + -1) = 0 Reorder the terms: 14 + 2x + -1(-2 + x)(-1 + x) = 0 Multiply (-2 + x) * (-1 + x) 14 + 2x + -1(-2(-1 + x) + x(-1 + x)) = 0 14 + 2x + -1((-1 * -2 + x * -2) + x(-1 + x)) = 0 14 + 2x + -1((2 + -2x) + x(-1 + x)) = 0 14 + 2x + -1(2 + -2x + (-1 * x + x * x)) = 0 14 + 2x + -1(2 + -2x + (-1x + x2)) = 0 Combine like terms: -2x + -1x = -3x 14 + 2x + -1(2 + -3x + x2) = 0 14 + 2x + (2 * -1 + -3x * -1 + x2 * -1) = 0 14 + 2x + (-2 + 3x + -1x2) = 0 Reorder the terms: 14 + -2 + 2x + 3x + -1x2 = 0 Combine like terms: 14 + -2 = 12 12 + 2x + 3x + -1x2 = 0 Combine like terms: 2x + 3x = 5x 12 + 5x + -1x2 = 0 Solving 12 + 5x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5x + x2 = 0 + 12 -5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -5x + x2 = 12 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 12 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + -5x + x2 = 18.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -2.5 = 4.272001873 Simplifying x + -2.5 = 4.272001873 Reorder the terms: -2.5 + x = 4.272001873 Solving -2.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.272001873 + 2.5 x = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 x = 6.772001873 Simplifying x = 6.772001873Subproblem 2
x + -2.5 = -4.272001873 Simplifying x + -2.5 = -4.272001873 Reorder the terms: -2.5 + x = -4.272001873 Solving -2.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.272001873 + 2.5 x = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 x = -1.772001873 Simplifying x = -1.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.772001873, -1.772001873}
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