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Simplifying 6x + -3x2 = 1 Solving 6x + -3x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 6x + -3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -2x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -2x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -2x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.3333333333 -2x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -2x + x2 = -0.3333333333 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 = -0.3333333333 + 1 Reorder the terms: 1 + -2x + x2 = -0.3333333333 + 1 Combine like terms: -0.3333333333 + 1 = 0.6666666667 1 + -2x + x2 = 0.6666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.6666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + -1) equal to 0.816496581 and -0.816496581.Subproblem 1
x + -1 = 0.816496581 Simplifying x + -1 = 0.816496581 Reorder the terms: -1 + x = 0.816496581 Solving -1 + x = 0.816496581 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 = 0.816496581 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.816496581 + 1 x = 0.816496581 + 1 Combine like terms: 0.816496581 + 1 = 1.816496581 x = 1.816496581 Simplifying x = 1.816496581Subproblem 2
x + -1 = -0.816496581 Simplifying x + -1 = -0.816496581 Reorder the terms: -1 + x = -0.816496581 Solving -1 + x = -0.816496581 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 = -0.816496581 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.816496581 + 1 x = -0.816496581 + 1 Combine like terms: -0.816496581 + 1 = 0.183503419 x = 0.183503419 Simplifying x = 0.183503419Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.816496581, 0.183503419}
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