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Simplifying (x + 2)(x + -5) = 7 Reorder the terms: (2 + x)(x + -5) = 7 Reorder the terms: (2 + x)(-5 + x) = 7 Multiply (2 + x) * (-5 + x) (2(-5 + x) + x(-5 + x)) = 7 ((-5 * 2 + x * 2) + x(-5 + x)) = 7 ((-10 + 2x) + x(-5 + x)) = 7 (-10 + 2x + (-5 * x + x * x)) = 7 (-10 + 2x + (-5x + x2)) = 7 Combine like terms: 2x + -5x = -3x (-10 + -3x + x2) = 7 Solving -10 + -3x + x2 = 7 Solving for variable 'x'. Reorder the terms: -10 + -7 + -3x + x2 = 7 + -7 Combine like terms: -10 + -7 = -17 -17 + -3x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -17 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -3x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -3x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -3x + x2 = 0 + 17 -3x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -3x + x2 = 17 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 17 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 17 + 2.25 Combine like terms: 17 + 2.25 = 19.25 2.25 + -3x + x2 = 19.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -1.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -1.5 = 4.387482194 Simplifying x + -1.5 = 4.387482194 Reorder the terms: -1.5 + x = 4.387482194 Solving -1.5 + x = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 4.387482194 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.387482194 + 1.5 x = 4.387482194 + 1.5 Combine like terms: 4.387482194 + 1.5 = 5.887482194 x = 5.887482194 Simplifying x = 5.887482194Subproblem 2
x + -1.5 = -4.387482194 Simplifying x + -1.5 = -4.387482194 Reorder the terms: -1.5 + x = -4.387482194 Solving -1.5 + x = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -4.387482194 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.387482194 + 1.5 x = -4.387482194 + 1.5 Combine like terms: -4.387482194 + 1.5 = -2.887482194 x = -2.887482194 Simplifying x = -2.887482194Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.887482194, -2.887482194}
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