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Simplifying 3x2 + -6x + -2 = 11 Reorder the terms: -2 + -6x + 3x2 = 11 Solving -2 + -6x + 3x2 = 11 Solving for variable 'x'. Reorder the terms: -2 + -11 + -6x + 3x2 = 11 + -11 Combine like terms: -2 + -11 = -13 -13 + -6x + 3x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -13 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -2x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -2x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 4.333333333 -2x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -2x + x2 = 4.333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 4.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 4.333333333 + 1 Combine like terms: 4.333333333 + 1 = 5.333333333 1 + -2x + x2 = 5.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (x + -1) equal to 2.309401077 and -2.309401077.Subproblem 1
x + -1 = 2.309401077 Simplifying x + -1 = 2.309401077 Reorder the terms: -1 + x = 2.309401077 Solving -1 + x = 2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.309401077 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.309401077 + 1 x = 2.309401077 + 1 Combine like terms: 2.309401077 + 1 = 3.309401077 x = 3.309401077 Simplifying x = 3.309401077Subproblem 2
x + -1 = -2.309401077 Simplifying x + -1 = -2.309401077 Reorder the terms: -1 + x = -2.309401077 Solving -1 + x = -2.309401077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.309401077 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.309401077 + 1 x = -2.309401077 + 1 Combine like terms: -2.309401077 + 1 = -1.309401077 x = -1.309401077 Simplifying x = -1.309401077Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.309401077, -1.309401077}
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