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Simplifying (3x + -1)(2x + 7) = 62 Reorder the terms: (-1 + 3x)(2x + 7) = 62 Reorder the terms: (-1 + 3x)(7 + 2x) = 62 Multiply (-1 + 3x) * (7 + 2x) (-1(7 + 2x) + 3x * (7 + 2x)) = 62 ((7 * -1 + 2x * -1) + 3x * (7 + 2x)) = 62 ((-7 + -2x) + 3x * (7 + 2x)) = 62 (-7 + -2x + (7 * 3x + 2x * 3x)) = 62 (-7 + -2x + (21x + 6x2)) = 62 Combine like terms: -2x + 21x = 19x (-7 + 19x + 6x2) = 62 Solving -7 + 19x + 6x2 = 62 Solving for variable 'x'. Reorder the terms: -7 + -62 + 19x + 6x2 = 62 + -62 Combine like terms: -7 + -62 = -69 -69 + 19x + 6x2 = 62 + -62 Combine like terms: 62 + -62 = 0 -69 + 19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -11.5 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 3.166666667x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 3.166666667x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 3.166666667x + x2 = 0 + 11.5 3.166666667x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 3.166666667x + x2 = 11.5 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 = 11.5 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = 11.5 + 2.506944447 Combine like terms: 11.5 + 2.506944447 = 14.006944447 2.506944447 + 3.166666667x + x2 = 14.006944447 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 14.006944447 Calculate the square root of the right side: 3.742585262 Break this problem into two subproblems by setting (x + 1.583333334) equal to 3.742585262 and -3.742585262.Subproblem 1
x + 1.583333334 = 3.742585262 Simplifying x + 1.583333334 = 3.742585262 Reorder the terms: 1.583333334 + x = 3.742585262 Solving 1.583333334 + x = 3.742585262 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 = 3.742585262 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 3.742585262 + -1.583333334 x = 3.742585262 + -1.583333334 Combine like terms: 3.742585262 + -1.583333334 = 2.159251928 x = 2.159251928 Simplifying x = 2.159251928Subproblem 2
x + 1.583333334 = -3.742585262 Simplifying x + 1.583333334 = -3.742585262 Reorder the terms: 1.583333334 + x = -3.742585262 Solving 1.583333334 + x = -3.742585262 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 = -3.742585262 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -3.742585262 + -1.583333334 x = -3.742585262 + -1.583333334 Combine like terms: -3.742585262 + -1.583333334 = -5.325918596 x = -5.325918596 Simplifying x = -5.325918596Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.159251928, -5.325918596}
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