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Simplifying 12x2 + -134 = 3x2 + -4 + -3x Reorder the terms: -134 + 12x2 = 3x2 + -4 + -3x Reorder the terms: -134 + 12x2 = -4 + -3x + 3x2 Solving -134 + 12x2 = -4 + -3x + 3x2 Solving for variable 'x'. Reorder the terms: -134 + 4 + 3x + 12x2 + -3x2 = -4 + -3x + 3x2 + 4 + 3x + -3x2 Combine like terms: -134 + 4 = -130 -130 + 3x + 12x2 + -3x2 = -4 + -3x + 3x2 + 4 + 3x + -3x2 Combine like terms: 12x2 + -3x2 = 9x2 -130 + 3x + 9x2 = -4 + -3x + 3x2 + 4 + 3x + -3x2 Reorder the terms: -130 + 3x + 9x2 = -4 + 4 + -3x + 3x + 3x2 + -3x2 Combine like terms: -4 + 4 = 0 -130 + 3x + 9x2 = 0 + -3x + 3x + 3x2 + -3x2 -130 + 3x + 9x2 = -3x + 3x + 3x2 + -3x2 Combine like terms: -3x + 3x = 0 -130 + 3x + 9x2 = 0 + 3x2 + -3x2 -130 + 3x + 9x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -130 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -14.44444444 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '14.44444444' to each side of the equation. -14.44444444 + 0.3333333333x + 14.44444444 + x2 = 0 + 14.44444444 Reorder the terms: -14.44444444 + 14.44444444 + 0.3333333333x + x2 = 0 + 14.44444444 Combine like terms: -14.44444444 + 14.44444444 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 14.44444444 0.3333333333x + x2 = 0 + 14.44444444 Combine like terms: 0 + 14.44444444 = 14.44444444 0.3333333333x + x2 = 14.44444444 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 = 14.44444444 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 14.44444444 + 0.02777777779 Combine like terms: 14.44444444 + 0.02777777779 = 14.47222221779 0.02777777779 + 0.3333333333x + x2 = 14.47222221779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 14.47222221779 Calculate the square root of the right side: 3.804237403 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 3.804237403 and -3.804237403.Subproblem 1
x + 0.1666666667 = 3.804237403 Simplifying x + 0.1666666667 = 3.804237403 Reorder the terms: 0.1666666667 + x = 3.804237403 Solving 0.1666666667 + x = 3.804237403 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 = 3.804237403 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 3.804237403 + -0.1666666667 x = 3.804237403 + -0.1666666667 Combine like terms: 3.804237403 + -0.1666666667 = 3.6375707363 x = 3.6375707363 Simplifying x = 3.6375707363Subproblem 2
x + 0.1666666667 = -3.804237403 Simplifying x + 0.1666666667 = -3.804237403 Reorder the terms: 0.1666666667 + x = -3.804237403 Solving 0.1666666667 + x = -3.804237403 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 = -3.804237403 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -3.804237403 + -0.1666666667 x = -3.804237403 + -0.1666666667 Combine like terms: -3.804237403 + -0.1666666667 = -3.9709040697 x = -3.9709040697 Simplifying x = -3.9709040697Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6375707363, -3.9709040697}
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