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Simplifying (x + 666)(x + 666) = 666 Reorder the terms: (666 + x)(x + 666) = 666 Reorder the terms: (666 + x)(666 + x) = 666 Multiply (666 + x) * (666 + x) (666(666 + x) + x(666 + x)) = 666 ((666 * 666 + x * 666) + x(666 + x)) = 666 ((443556 + 666x) + x(666 + x)) = 666 (443556 + 666x + (666 * x + x * x)) = 666 (443556 + 666x + (666x + x2)) = 666 Combine like terms: 666x + 666x = 1332x (443556 + 1332x + x2) = 666 Solving 443556 + 1332x + x2 = 666 Solving for variable 'x'. Reorder the terms: 443556 + -666 + 1332x + x2 = 666 + -666 Combine like terms: 443556 + -666 = 442890 442890 + 1332x + x2 = 666 + -666 Combine like terms: 666 + -666 = 0 442890 + 1332x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-442890' to each side of the equation. 442890 + 1332x + -442890 + x2 = 0 + -442890 Reorder the terms: 442890 + -442890 + 1332x + x2 = 0 + -442890 Combine like terms: 442890 + -442890 = 0 0 + 1332x + x2 = 0 + -442890 1332x + x2 = 0 + -442890 Combine like terms: 0 + -442890 = -442890 1332x + x2 = -442890 The x term is 1332x. Take half its coefficient (666). Square it (443556) and add it to both sides. Add '443556' to each side of the equation. 1332x + 443556 + x2 = -442890 + 443556 Reorder the terms: 443556 + 1332x + x2 = -442890 + 443556 Combine like terms: -442890 + 443556 = 666 443556 + 1332x + x2 = 666 Factor a perfect square on the left side: (x + 666)(x + 666) = 666 Calculate the square root of the right side: 25.806975801 Break this problem into two subproblems by setting (x + 666) equal to 25.806975801 and -25.806975801.Subproblem 1
x + 666 = 25.806975801 Simplifying x + 666 = 25.806975801 Reorder the terms: 666 + x = 25.806975801 Solving 666 + x = 25.806975801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-666' to each side of the equation. 666 + -666 + x = 25.806975801 + -666 Combine like terms: 666 + -666 = 0 0 + x = 25.806975801 + -666 x = 25.806975801 + -666 Combine like terms: 25.806975801 + -666 = -640.193024199 x = -640.193024199 Simplifying x = -640.193024199Subproblem 2
x + 666 = -25.806975801 Simplifying x + 666 = -25.806975801 Reorder the terms: 666 + x = -25.806975801 Solving 666 + x = -25.806975801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-666' to each side of the equation. 666 + -666 + x = -25.806975801 + -666 Combine like terms: 666 + -666 = 0 0 + x = -25.806975801 + -666 x = -25.806975801 + -666 Combine like terms: -25.806975801 + -666 = -691.806975801 x = -691.806975801 Simplifying x = -691.806975801Solution
The solution to the problem is based on the solutions from the subproblems. x = {-640.193024199, -691.806975801}
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