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Simplifying (x + 2)(-19 + x) = 227 Reorder the terms: (2 + x)(-19 + x) = 227 Multiply (2 + x) * (-19 + x) (2(-19 + x) + x(-19 + x)) = 227 ((-19 * 2 + x * 2) + x(-19 + x)) = 227 ((-38 + 2x) + x(-19 + x)) = 227 (-38 + 2x + (-19 * x + x * x)) = 227 (-38 + 2x + (-19x + x2)) = 227 Combine like terms: 2x + -19x = -17x (-38 + -17x + x2) = 227 Solving -38 + -17x + x2 = 227 Solving for variable 'x'. Reorder the terms: -38 + -227 + -17x + x2 = 227 + -227 Combine like terms: -38 + -227 = -265 -265 + -17x + x2 = 227 + -227 Combine like terms: 227 + -227 = 0 -265 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '265' to each side of the equation. -265 + -17x + 265 + x2 = 0 + 265 Reorder the terms: -265 + 265 + -17x + x2 = 0 + 265 Combine like terms: -265 + 265 = 0 0 + -17x + x2 = 0 + 265 -17x + x2 = 0 + 265 Combine like terms: 0 + 265 = 265 -17x + x2 = 265 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 265 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 265 + 72.25 Combine like terms: 265 + 72.25 = 337.25 72.25 + -17x + x2 = 337.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 337.25 Calculate the square root of the right side: 18.364367672 Break this problem into two subproblems by setting (x + -8.5) equal to 18.364367672 and -18.364367672.Subproblem 1
x + -8.5 = 18.364367672 Simplifying x + -8.5 = 18.364367672 Reorder the terms: -8.5 + x = 18.364367672 Solving -8.5 + x = 18.364367672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 18.364367672 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 18.364367672 + 8.5 x = 18.364367672 + 8.5 Combine like terms: 18.364367672 + 8.5 = 26.864367672 x = 26.864367672 Simplifying x = 26.864367672Subproblem 2
x + -8.5 = -18.364367672 Simplifying x + -8.5 = -18.364367672 Reorder the terms: -8.5 + x = -18.364367672 Solving -8.5 + x = -18.364367672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -18.364367672 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -18.364367672 + 8.5 x = -18.364367672 + 8.5 Combine like terms: -18.364367672 + 8.5 = -9.864367672 x = -9.864367672 Simplifying x = -9.864367672Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.864367672, -9.864367672}
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