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Simplifying 36x2 + 12x + 1 = 18 Reorder the terms: 1 + 12x + 36x2 = 18 Solving 1 + 12x + 36x2 = 18 Solving for variable 'x'. Reorder the terms: 1 + -18 + 12x + 36x2 = 18 + -18 Combine like terms: 1 + -18 = -17 -17 + 12x + 36x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -17 + 12x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.4722222222 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.4722222222' to each side of the equation. -0.4722222222 + 0.3333333333x + 0.4722222222 + x2 = 0 + 0.4722222222 Reorder the terms: -0.4722222222 + 0.4722222222 + 0.3333333333x + x2 = 0 + 0.4722222222 Combine like terms: -0.4722222222 + 0.4722222222 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.4722222222 0.3333333333x + x2 = 0 + 0.4722222222 Combine like terms: 0 + 0.4722222222 = 0.4722222222 0.3333333333x + x2 = 0.4722222222 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.4722222222 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.4722222222 + 0.02777777779 Combine like terms: 0.4722222222 + 0.02777777779 = 0.49999999999 0.02777777779 + 0.3333333333x + x2 = 0.49999999999 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.49999999999 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.707106781 and -0.707106781.Subproblem 1
x + 0.1666666667 = 0.707106781 Simplifying x + 0.1666666667 = 0.707106781 Reorder the terms: 0.1666666667 + x = 0.707106781 Solving 0.1666666667 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.707106781 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.707106781 + -0.1666666667 x = 0.707106781 + -0.1666666667 Combine like terms: 0.707106781 + -0.1666666667 = 0.5404401143 x = 0.5404401143 Simplifying x = 0.5404401143Subproblem 2
x + 0.1666666667 = -0.707106781 Simplifying x + 0.1666666667 = -0.707106781 Reorder the terms: 0.1666666667 + x = -0.707106781 Solving 0.1666666667 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.707106781 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.707106781 + -0.1666666667 x = -0.707106781 + -0.1666666667 Combine like terms: -0.707106781 + -0.1666666667 = -0.8737734477 x = -0.8737734477 Simplifying x = -0.8737734477Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5404401143, -0.8737734477}
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