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Simplifying 6X2 + 2X = 15 Reorder the terms: 2X + 6X2 = 15 Solving 2X + 6X2 = 15 Solving for variable 'X'. Reorder the terms: -15 + 2X + 6X2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 2X + 6X2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + 0.3333333333X + X2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.3333333333X + 2.5 + X2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.3333333333X + X2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.3333333333X + X2 = 0 + 2.5 0.3333333333X + X2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.3333333333X + X2 = 2.5 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 = 2.5 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333X + X2 = 2.5 + 0.02777777779 Combine like terms: 2.5 + 0.02777777779 = 2.52777777779 0.02777777779 + 0.3333333333X + X2 = 2.52777777779 Factor a perfect square on the left side: (X + 0.1666666667)(X + 0.1666666667) = 2.52777777779 Calculate the square root of the right side: 1.589898669 Break this problem into two subproblems by setting (X + 0.1666666667) equal to 1.589898669 and -1.589898669.Subproblem 1
X + 0.1666666667 = 1.589898669 Simplifying X + 0.1666666667 = 1.589898669 Reorder the terms: 0.1666666667 + X = 1.589898669 Solving 0.1666666667 + X = 1.589898669 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 = 1.589898669 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + X = 1.589898669 + -0.1666666667 X = 1.589898669 + -0.1666666667 Combine like terms: 1.589898669 + -0.1666666667 = 1.4232320023 X = 1.4232320023 Simplifying X = 1.4232320023Subproblem 2
X + 0.1666666667 = -1.589898669 Simplifying X + 0.1666666667 = -1.589898669 Reorder the terms: 0.1666666667 + X = -1.589898669 Solving 0.1666666667 + X = -1.589898669 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 = -1.589898669 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + X = -1.589898669 + -0.1666666667 X = -1.589898669 + -0.1666666667 Combine like terms: -1.589898669 + -0.1666666667 = -1.7565653357 X = -1.7565653357 Simplifying X = -1.7565653357Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.4232320023, -1.7565653357}
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