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Simplifying 3x + -1 = 10 + -9x2 Reorder the terms: -1 + 3x = 10 + -9x2 Solving -1 + 3x = 10 + -9x2 Solving for variable 'x'. Reorder the terms: -1 + -10 + 3x + 9x2 = 10 + -9x2 + -10 + 9x2 Combine like terms: -1 + -10 = -11 -11 + 3x + 9x2 = 10 + -9x2 + -10 + 9x2 Reorder the terms: -11 + 3x + 9x2 = 10 + -10 + -9x2 + 9x2 Combine like terms: 10 + -10 = 0 -11 + 3x + 9x2 = 0 + -9x2 + 9x2 -11 + 3x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -11 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.222222222 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 0.3333333333x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 0.3333333333x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + 1.222222222 0.3333333333x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 0.3333333333x + x2 = 1.222222222 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 = 1.222222222 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 1.222222222 + 0.02777777779 Combine like terms: 1.222222222 + 0.02777777779 = 1.24999999979 0.02777777779 + 0.3333333333x + x2 = 1.24999999979 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 1.24999999979 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 0.1666666667 = 1.118033989 Simplifying x + 0.1666666667 = 1.118033989 Reorder the terms: 0.1666666667 + x = 1.118033989 Solving 0.1666666667 + x = 1.118033989 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 = 1.118033989 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.118033989 + -0.1666666667 x = 1.118033989 + -0.1666666667 Combine like terms: 1.118033989 + -0.1666666667 = 0.9513673223 x = 0.9513673223 Simplifying x = 0.9513673223Subproblem 2
x + 0.1666666667 = -1.118033989 Simplifying x + 0.1666666667 = -1.118033989 Reorder the terms: 0.1666666667 + x = -1.118033989 Solving 0.1666666667 + x = -1.118033989 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 = -1.118033989 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.118033989 + -0.1666666667 x = -1.118033989 + -0.1666666667 Combine like terms: -1.118033989 + -0.1666666667 = -1.2847006557 x = -1.2847006557 Simplifying x = -1.2847006557Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9513673223, -1.2847006557}
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