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Simplifying x2 + 0.66667x + -0.66667 = 0 Reorder the terms: -0.66667 + 0.66667x + x2 = 0 Solving -0.66667 + 0.66667x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.66667' to each side of the equation. -0.66667 + 0.66667x + 0.66667 + x2 = 0 + 0.66667 Reorder the terms: -0.66667 + 0.66667 + 0.66667x + x2 = 0 + 0.66667 Combine like terms: -0.66667 + 0.66667 = 0.00000 0.00000 + 0.66667x + x2 = 0 + 0.66667 0.66667x + x2 = 0 + 0.66667 Combine like terms: 0 + 0.66667 = 0.66667 0.66667x + x2 = 0.66667 The x term is 0.66667x. Take half its coefficient (0.333335). Square it (0.1111122222) and add it to both sides. Add '0.1111122222' to each side of the equation. 0.66667x + 0.1111122222 + x2 = 0.66667 + 0.1111122222 Reorder the terms: 0.1111122222 + 0.66667x + x2 = 0.66667 + 0.1111122222 Combine like terms: 0.66667 + 0.1111122222 = 0.7777822222 0.1111122222 + 0.66667x + x2 = 0.7777822222 Factor a perfect square on the left side: (x + 0.333335)(x + 0.333335) = 0.7777822222 Calculate the square root of the right side: 0.881919623 Break this problem into two subproblems by setting (x + 0.333335) equal to 0.881919623 and -0.881919623.Subproblem 1
x + 0.333335 = 0.881919623 Simplifying x + 0.333335 = 0.881919623 Reorder the terms: 0.333335 + x = 0.881919623 Solving 0.333335 + x = 0.881919623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.333335' to each side of the equation. 0.333335 + -0.333335 + x = 0.881919623 + -0.333335 Combine like terms: 0.333335 + -0.333335 = 0.000000 0.000000 + x = 0.881919623 + -0.333335 x = 0.881919623 + -0.333335 Combine like terms: 0.881919623 + -0.333335 = 0.548584623 x = 0.548584623 Simplifying x = 0.548584623Subproblem 2
x + 0.333335 = -0.881919623 Simplifying x + 0.333335 = -0.881919623 Reorder the terms: 0.333335 + x = -0.881919623 Solving 0.333335 + x = -0.881919623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.333335' to each side of the equation. 0.333335 + -0.333335 + x = -0.881919623 + -0.333335 Combine like terms: 0.333335 + -0.333335 = 0.000000 0.000000 + x = -0.881919623 + -0.333335 x = -0.881919623 + -0.333335 Combine like terms: -0.881919623 + -0.333335 = -1.215254623 x = -1.215254623 Simplifying x = -1.215254623Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.548584623, -1.215254623}
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