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Simplifying 6x + -1(2x + -1)(2x + 1) = 2 Reorder the terms: 6x + -1(-1 + 2x)(2x + 1) = 2 Reorder the terms: 6x + -1(-1 + 2x)(1 + 2x) = 2 Multiply (-1 + 2x) * (1 + 2x) 6x + -1(-1(1 + 2x) + 2x * (1 + 2x)) = 2 6x + -1((1 * -1 + 2x * -1) + 2x * (1 + 2x)) = 2 6x + -1((-1 + -2x) + 2x * (1 + 2x)) = 2 6x + -1(-1 + -2x + (1 * 2x + 2x * 2x)) = 2 6x + -1(-1 + -2x + (2x + 4x2)) = 2 Combine like terms: -2x + 2x = 0 6x + -1(-1 + 0 + 4x2) = 2 6x + -1(-1 + 4x2) = 2 6x + (-1 * -1 + 4x2 * -1) = 2 6x + (1 + -4x2) = 2 Reorder the terms: 1 + 6x + -4x2 = 2 Solving 1 + 6x + -4x2 = 2 Solving for variable 'x'. Reorder the terms: 1 + -2 + 6x + -4x2 = 2 + -2 Combine like terms: 1 + -2 = -1 -1 + 6x + -4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -1 + 6x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.5x + x2 = 0 + -0.25 -1.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.5x + x2 = -0.25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.25 + 0.5625 Combine like terms: -0.25 + 0.5625 = 0.3125 0.5625 + -1.5x + x2 = 0.3125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x + -0.75) equal to 0.559016994 and -0.559016994.Subproblem 1
x + -0.75 = 0.559016994 Simplifying x + -0.75 = 0.559016994 Reorder the terms: -0.75 + x = 0.559016994 Solving -0.75 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.559016994 + 0.75 x = 0.559016994 + 0.75 Combine like terms: 0.559016994 + 0.75 = 1.309016994 x = 1.309016994 Simplifying x = 1.309016994Subproblem 2
x + -0.75 = -0.559016994 Simplifying x + -0.75 = -0.559016994 Reorder the terms: -0.75 + x = -0.559016994 Solving -0.75 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.559016994 + 0.75 x = -0.559016994 + 0.75 Combine like terms: -0.559016994 + 0.75 = 0.190983006 x = 0.190983006 Simplifying x = 0.190983006Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.309016994, 0.190983006}
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