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Simplifying (x + 64)(x + -222) = 666 Reorder the terms: (64 + x)(x + -222) = 666 Reorder the terms: (64 + x)(-222 + x) = 666 Multiply (64 + x) * (-222 + x) (64(-222 + x) + x(-222 + x)) = 666 ((-222 * 64 + x * 64) + x(-222 + x)) = 666 ((-14208 + 64x) + x(-222 + x)) = 666 (-14208 + 64x + (-222 * x + x * x)) = 666 (-14208 + 64x + (-222x + x2)) = 666 Combine like terms: 64x + -222x = -158x (-14208 + -158x + x2) = 666 Solving -14208 + -158x + x2 = 666 Solving for variable 'x'. Reorder the terms: -14208 + -666 + -158x + x2 = 666 + -666 Combine like terms: -14208 + -666 = -14874 -14874 + -158x + x2 = 666 + -666 Combine like terms: 666 + -666 = 0 -14874 + -158x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14874' to each side of the equation. -14874 + -158x + 14874 + x2 = 0 + 14874 Reorder the terms: -14874 + 14874 + -158x + x2 = 0 + 14874 Combine like terms: -14874 + 14874 = 0 0 + -158x + x2 = 0 + 14874 -158x + x2 = 0 + 14874 Combine like terms: 0 + 14874 = 14874 -158x + x2 = 14874 The x term is -158x. Take half its coefficient (-79). Square it (6241) and add it to both sides. Add '6241' to each side of the equation. -158x + 6241 + x2 = 14874 + 6241 Reorder the terms: 6241 + -158x + x2 = 14874 + 6241 Combine like terms: 14874 + 6241 = 21115 6241 + -158x + x2 = 21115 Factor a perfect square on the left side: (x + -79)(x + -79) = 21115 Calculate the square root of the right side: 145.31001342 Break this problem into two subproblems by setting (x + -79) equal to 145.31001342 and -145.31001342.Subproblem 1
x + -79 = 145.31001342 Simplifying x + -79 = 145.31001342 Reorder the terms: -79 + x = 145.31001342 Solving -79 + x = 145.31001342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '79' to each side of the equation. -79 + 79 + x = 145.31001342 + 79 Combine like terms: -79 + 79 = 0 0 + x = 145.31001342 + 79 x = 145.31001342 + 79 Combine like terms: 145.31001342 + 79 = 224.31001342 x = 224.31001342 Simplifying x = 224.31001342Subproblem 2
x + -79 = -145.31001342 Simplifying x + -79 = -145.31001342 Reorder the terms: -79 + x = -145.31001342 Solving -79 + x = -145.31001342 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '79' to each side of the equation. -79 + 79 + x = -145.31001342 + 79 Combine like terms: -79 + 79 = 0 0 + x = -145.31001342 + 79 x = -145.31001342 + 79 Combine like terms: -145.31001342 + 79 = -66.31001342 x = -66.31001342 Simplifying x = -66.31001342Solution
The solution to the problem is based on the solutions from the subproblems. x = {224.31001342, -66.31001342}
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