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Simplifying (6x + 5)(x + -4) = 6 Reorder the terms: (5 + 6x)(x + -4) = 6 Reorder the terms: (5 + 6x)(-4 + x) = 6 Multiply (5 + 6x) * (-4 + x) (5(-4 + x) + 6x * (-4 + x)) = 6 ((-4 * 5 + x * 5) + 6x * (-4 + x)) = 6 ((-20 + 5x) + 6x * (-4 + x)) = 6 (-20 + 5x + (-4 * 6x + x * 6x)) = 6 (-20 + 5x + (-24x + 6x2)) = 6 Combine like terms: 5x + -24x = -19x (-20 + -19x + 6x2) = 6 Solving -20 + -19x + 6x2 = 6 Solving for variable 'x'. Reorder the terms: -20 + -6 + -19x + 6x2 = 6 + -6 Combine like terms: -20 + -6 = -26 -26 + -19x + 6x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -26 + -19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.333333333 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -3.166666667x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -3.166666667x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0 + 4.333333333 -3.166666667x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -3.166666667x + x2 = 4.333333333 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 4.333333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 4.333333333 + 2.506944447 Combine like terms: 4.333333333 + 2.506944447 = 6.84027778 2.506944447 + -3.166666667x + x2 = 6.84027778 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 6.84027778 Calculate the square root of the right side: 2.615392472 Break this problem into two subproblems by setting (x + -1.583333334) equal to 2.615392472 and -2.615392472.Subproblem 1
x + -1.583333334 = 2.615392472 Simplifying x + -1.583333334 = 2.615392472 Reorder the terms: -1.583333334 + x = 2.615392472 Solving -1.583333334 + x = 2.615392472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 2.615392472 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 2.615392472 + 1.583333334 x = 2.615392472 + 1.583333334 Combine like terms: 2.615392472 + 1.583333334 = 4.198725806 x = 4.198725806 Simplifying x = 4.198725806Subproblem 2
x + -1.583333334 = -2.615392472 Simplifying x + -1.583333334 = -2.615392472 Reorder the terms: -1.583333334 + x = -2.615392472 Solving -1.583333334 + x = -2.615392472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -2.615392472 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -2.615392472 + 1.583333334 x = -2.615392472 + 1.583333334 Combine like terms: -2.615392472 + 1.583333334 = -1.032059138 x = -1.032059138 Simplifying x = -1.032059138Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.198725806, -1.032059138}
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