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Simplifying 3x(7x + -2) = 4 Reorder the terms: 3x(-2 + 7x) = 4 (-2 * 3x + 7x * 3x) = 4 (-6x + 21x2) = 4 Solving -6x + 21x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -6x + 21x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -6x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.1904761905 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.1904761905' to each side of the equation. -0.1904761905 + -0.2857142857x + 0.1904761905 + x2 = 0 + 0.1904761905 Reorder the terms: -0.1904761905 + 0.1904761905 + -0.2857142857x + x2 = 0 + 0.1904761905 Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.1904761905 -0.2857142857x + x2 = 0 + 0.1904761905 Combine like terms: 0 + 0.1904761905 = 0.1904761905 -0.2857142857x + x2 = 0.1904761905 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 = 0.1904761905 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.1904761905 + 0.02040816328 Combine like terms: 0.1904761905 + 0.02040816328 = 0.21088435378 0.02040816328 + -0.2857142857x + x2 = 0.21088435378 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.21088435378 Calculate the square root of the right side: 0.459221465 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.459221465 and -0.459221465.Subproblem 1
x + -0.1428571429 = 0.459221465 Simplifying x + -0.1428571429 = 0.459221465 Reorder the terms: -0.1428571429 + x = 0.459221465 Solving -0.1428571429 + x = 0.459221465 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 = 0.459221465 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.459221465 + 0.1428571429 x = 0.459221465 + 0.1428571429 Combine like terms: 0.459221465 + 0.1428571429 = 0.6020786079 x = 0.6020786079 Simplifying x = 0.6020786079Subproblem 2
x + -0.1428571429 = -0.459221465 Simplifying x + -0.1428571429 = -0.459221465 Reorder the terms: -0.1428571429 + x = -0.459221465 Solving -0.1428571429 + x = -0.459221465 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 = -0.459221465 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.459221465 + 0.1428571429 x = -0.459221465 + 0.1428571429 Combine like terms: -0.459221465 + 0.1428571429 = -0.3163643221 x = -0.3163643221 Simplifying x = -0.3163643221Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6020786079, -0.3163643221}
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