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Simplifying 3x(2x + -1) = 1 Reorder the terms: 3x(-1 + 2x) = 1 (-1 * 3x + 2x * 3x) = 1 (-3x + 6x2) = 1 Solving -3x + 6x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -3x + 6x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.5x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.5x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.5x + x2 = 0 + 0.1666666667 -0.5x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.5x + x2 = 0.1666666667 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.1666666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.1666666667 + 0.0625 Combine like terms: 0.1666666667 + 0.0625 = 0.2291666667 0.0625 + -0.5x + x2 = 0.2291666667 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.2291666667 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (x + -0.25) equal to 0.478713554 and -0.478713554.Subproblem 1
x + -0.25 = 0.478713554 Simplifying x + -0.25 = 0.478713554 Reorder the terms: -0.25 + x = 0.478713554 Solving -0.25 + x = 0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.478713554 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.478713554 + 0.25 x = 0.478713554 + 0.25 Combine like terms: 0.478713554 + 0.25 = 0.728713554 x = 0.728713554 Simplifying x = 0.728713554Subproblem 2
x + -0.25 = -0.478713554 Simplifying x + -0.25 = -0.478713554 Reorder the terms: -0.25 + x = -0.478713554 Solving -0.25 + x = -0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.478713554 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.478713554 + 0.25 x = -0.478713554 + 0.25 Combine like terms: -0.478713554 + 0.25 = -0.228713554 x = -0.228713554 Simplifying x = -0.228713554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.728713554, -0.228713554}
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