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Simplifying 3x(7x + -2) = 20 Reorder the terms: 3x(-2 + 7x) = 20 (-2 * 3x + 7x * 3x) = 20 (-6x + 21x2) = 20 Solving -6x + 21x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -6x + 21x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -6x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.9523809524 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.9523809524' to each side of the equation. -0.9523809524 + -0.2857142857x + 0.9523809524 + x2 = 0 + 0.9523809524 Reorder the terms: -0.9523809524 + 0.9523809524 + -0.2857142857x + x2 = 0 + 0.9523809524 Combine like terms: -0.9523809524 + 0.9523809524 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.9523809524 -0.2857142857x + x2 = 0 + 0.9523809524 Combine like terms: 0 + 0.9523809524 = 0.9523809524 -0.2857142857x + x2 = 0.9523809524 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.9523809524 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.9523809524 + 0.02040816328 Combine like terms: 0.9523809524 + 0.02040816328 = 0.97278911568 0.02040816328 + -0.2857142857x + x2 = 0.97278911568 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.97278911568 Calculate the square root of the right side: 0.986300723 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.986300723 and -0.986300723.Subproblem 1
x + -0.1428571429 = 0.986300723 Simplifying x + -0.1428571429 = 0.986300723 Reorder the terms: -0.1428571429 + x = 0.986300723 Solving -0.1428571429 + x = 0.986300723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.986300723 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.986300723 + 0.1428571429 x = 0.986300723 + 0.1428571429 Combine like terms: 0.986300723 + 0.1428571429 = 1.1291578659 x = 1.1291578659 Simplifying x = 1.1291578659Subproblem 2
x + -0.1428571429 = -0.986300723 Simplifying x + -0.1428571429 = -0.986300723 Reorder the terms: -0.1428571429 + x = -0.986300723 Solving -0.1428571429 + x = -0.986300723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.986300723 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.986300723 + 0.1428571429 x = -0.986300723 + 0.1428571429 Combine like terms: -0.986300723 + 0.1428571429 = -0.8434435801 x = -0.8434435801 Simplifying x = -0.8434435801Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1291578659, -0.8434435801}
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