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Simplifying (x + 2)(x + -9) = 104 Reorder the terms: (2 + x)(x + -9) = 104 Reorder the terms: (2 + x)(-9 + x) = 104 Multiply (2 + x) * (-9 + x) (2(-9 + x) + x(-9 + x)) = 104 ((-9 * 2 + x * 2) + x(-9 + x)) = 104 ((-18 + 2x) + x(-9 + x)) = 104 (-18 + 2x + (-9 * x + x * x)) = 104 (-18 + 2x + (-9x + x2)) = 104 Combine like terms: 2x + -9x = -7x (-18 + -7x + x2) = 104 Solving -18 + -7x + x2 = 104 Solving for variable 'x'. Reorder the terms: -18 + -104 + -7x + x2 = 104 + -104 Combine like terms: -18 + -104 = -122 -122 + -7x + x2 = 104 + -104 Combine like terms: 104 + -104 = 0 -122 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + -7x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + -7x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + -7x + x2 = 0 + 122 -7x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 -7x + x2 = 122 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 122 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 122 + 12.25 Combine like terms: 122 + 12.25 = 134.25 12.25 + -7x + x2 = 134.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + -3.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + -3.5 = 11.586630226 Simplifying x + -3.5 = 11.586630226 Reorder the terms: -3.5 + x = 11.586630226 Solving -3.5 + x = 11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 11.586630226 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 11.586630226 + 3.5 x = 11.586630226 + 3.5 Combine like terms: 11.586630226 + 3.5 = 15.086630226 x = 15.086630226 Simplifying x = 15.086630226Subproblem 2
x + -3.5 = -11.586630226 Simplifying x + -3.5 = -11.586630226 Reorder the terms: -3.5 + x = -11.586630226 Solving -3.5 + x = -11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -11.586630226 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -11.586630226 + 3.5 x = -11.586630226 + 3.5 Combine like terms: -11.586630226 + 3.5 = -8.086630226 x = -8.086630226 Simplifying x = -8.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.086630226, -8.086630226}
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