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Simplifying 11 = (3x + 2)(2x + -8) Reorder the terms: 11 = (2 + 3x)(2x + -8) Reorder the terms: 11 = (2 + 3x)(-8 + 2x) Multiply (2 + 3x) * (-8 + 2x) 11 = (2(-8 + 2x) + 3x * (-8 + 2x)) 11 = ((-8 * 2 + 2x * 2) + 3x * (-8 + 2x)) 11 = ((-16 + 4x) + 3x * (-8 + 2x)) 11 = (-16 + 4x + (-8 * 3x + 2x * 3x)) 11 = (-16 + 4x + (-24x + 6x2)) Combine like terms: 4x + -24x = -20x 11 = (-16 + -20x + 6x2) Solving 11 = -16 + -20x + 6x2 Solving for variable 'x'. Combine like terms: 11 + 16 = 27 27 + 20x + -6x2 = -16 + -20x + 6x2 + 16 + 20x + -6x2 Reorder the terms: 27 + 20x + -6x2 = -16 + 16 + -20x + 20x + 6x2 + -6x2 Combine like terms: -16 + 16 = 0 27 + 20x + -6x2 = 0 + -20x + 20x + 6x2 + -6x2 27 + 20x + -6x2 = -20x + 20x + 6x2 + -6x2 Combine like terms: -20x + 20x = 0 27 + 20x + -6x2 = 0 + 6x2 + -6x2 27 + 20x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 27 + 20x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -4.5 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -3.333333333x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -3.333333333x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -3.333333333x + x2 = 0 + 4.5 -3.333333333x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -3.333333333x + x2 = 4.5 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 4.5 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 4.5 + 2.777777779 Combine like terms: 4.5 + 2.777777779 = 7.277777779 2.777777779 + -3.333333333x + x2 = 7.277777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 7.277777779 Calculate the square root of the right side: 2.697735676 Break this problem into two subproblems by setting (x + -1.666666667) equal to 2.697735676 and -2.697735676.Subproblem 1
x + -1.666666667 = 2.697735676 Simplifying x + -1.666666667 = 2.697735676 Reorder the terms: -1.666666667 + x = 2.697735676 Solving -1.666666667 + x = 2.697735676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 2.697735676 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.697735676 + 1.666666667 x = 2.697735676 + 1.666666667 Combine like terms: 2.697735676 + 1.666666667 = 4.364402343 x = 4.364402343 Simplifying x = 4.364402343Subproblem 2
x + -1.666666667 = -2.697735676 Simplifying x + -1.666666667 = -2.697735676 Reorder the terms: -1.666666667 + x = -2.697735676 Solving -1.666666667 + x = -2.697735676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -2.697735676 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.697735676 + 1.666666667 x = -2.697735676 + 1.666666667 Combine like terms: -2.697735676 + 1.666666667 = -1.031069009 x = -1.031069009 Simplifying x = -1.031069009Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.364402343, -1.031069009}
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