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Simplifying 12x2 + 7x = 6 Reorder the terms: 7x + 12x2 = 6 Solving 7x + 12x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 7x + 12x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.5833333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.5833333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.5833333333x + x2 = 0 + 0.5 0.5833333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.5833333333x + x2 = 0.5 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = 0.5 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = 0.5 + 0.08506944446 Combine like terms: 0.5 + 0.08506944446 = 0.58506944446 0.08506944446 + 0.5833333333x + x2 = 0.58506944446 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = 0.58506944446 Calculate the square root of the right side: 0.764898323 Break this problem into two subproblems by setting (x + 0.2916666667) equal to 0.764898323 and -0.764898323.Subproblem 1
x + 0.2916666667 = 0.764898323 Simplifying x + 0.2916666667 = 0.764898323 Reorder the terms: 0.2916666667 + x = 0.764898323 Solving 0.2916666667 + x = 0.764898323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = 0.764898323 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = 0.764898323 + -0.2916666667 x = 0.764898323 + -0.2916666667 Combine like terms: 0.764898323 + -0.2916666667 = 0.4732316563 x = 0.4732316563 Simplifying x = 0.4732316563Subproblem 2
x + 0.2916666667 = -0.764898323 Simplifying x + 0.2916666667 = -0.764898323 Reorder the terms: 0.2916666667 + x = -0.764898323 Solving 0.2916666667 + x = -0.764898323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = -0.764898323 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = -0.764898323 + -0.2916666667 x = -0.764898323 + -0.2916666667 Combine like terms: -0.764898323 + -0.2916666667 = -1.0565649897 x = -1.0565649897 Simplifying x = -1.0565649897Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4732316563, -1.0565649897}
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