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Simplifying 3x * x + -6x + -2 = 0 Multiply x * x 3x2 + -6x + -2 = 0 Reorder the terms: -2 + -6x + 3x2 = 0 Solving -2 + -6x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -2x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -2x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -2x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.6666666667 -2x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -2x + x2 = 0.6666666667 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 = 0.6666666667 + 1 Reorder the terms: 1 + -2x + x2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + -2x + x2 = 1.6666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (x + -1) equal to 1.290994449 and -1.290994449.Subproblem 1
x + -1 = 1.290994449 Simplifying x + -1 = 1.290994449 Reorder the terms: -1 + x = 1.290994449 Solving -1 + x = 1.290994449 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 = 1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.290994449 + 1 x = 1.290994449 + 1 Combine like terms: 1.290994449 + 1 = 2.290994449 x = 2.290994449 Simplifying x = 2.290994449Subproblem 2
x + -1 = -1.290994449 Simplifying x + -1 = -1.290994449 Reorder the terms: -1 + x = -1.290994449 Solving -1 + x = -1.290994449 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 = -1.290994449 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.290994449 + 1 x = -1.290994449 + 1 Combine like terms: -1.290994449 + 1 = -0.290994449 x = -0.290994449 Simplifying x = -0.290994449Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.290994449, -0.290994449}
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