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Simplifying 6x(2x + -5) = 2x + 11 Reorder the terms: 6x(-5 + 2x) = 2x + 11 (-5 * 6x + 2x * 6x) = 2x + 11 (-30x + 12x2) = 2x + 11 Reorder the terms: -30x + 12x2 = 11 + 2x Solving -30x + 12x2 = 11 + 2x Solving for variable 'x'. Reorder the terms: -11 + -30x + -2x + 12x2 = 11 + 2x + -11 + -2x Combine like terms: -30x + -2x = -32x -11 + -32x + 12x2 = 11 + 2x + -11 + -2x Reorder the terms: -11 + -32x + 12x2 = 11 + -11 + 2x + -2x Combine like terms: 11 + -11 = 0 -11 + -32x + 12x2 = 0 + 2x + -2x -11 + -32x + 12x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -11 + -32x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.9166666667 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + -2.666666667x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + -2.666666667x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + 0.9166666667 -2.666666667x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 -2.666666667x + x2 = 0.9166666667 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.9166666667 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.9166666667 + 1.777777780 Combine like terms: 0.9166666667 + 1.777777780 = 2.6944444467 1.777777780 + -2.666666667x + x2 = 2.6944444467 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.6944444467 Calculate the square root of the right side: 1.641476301 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.641476301 and -1.641476301.Subproblem 1
x + -1.333333334 = 1.641476301 Simplifying x + -1.333333334 = 1.641476301 Reorder the terms: -1.333333334 + x = 1.641476301 Solving -1.333333334 + x = 1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.641476301 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.641476301 + 1.333333334 x = 1.641476301 + 1.333333334 Combine like terms: 1.641476301 + 1.333333334 = 2.974809635 x = 2.974809635 Simplifying x = 2.974809635Subproblem 2
x + -1.333333334 = -1.641476301 Simplifying x + -1.333333334 = -1.641476301 Reorder the terms: -1.333333334 + x = -1.641476301 Solving -1.333333334 + x = -1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.641476301 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.641476301 + 1.333333334 x = -1.641476301 + 1.333333334 Combine like terms: -1.641476301 + 1.333333334 = -0.308142967 x = -0.308142967 Simplifying x = -0.308142967Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.974809635, -0.308142967}
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