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Simplifying 6(1 + -3x) + 7x(7 + -1x) = 0 (1 * 6 + -3x * 6) + 7x(7 + -1x) = 0 (6 + -18x) + 7x(7 + -1x) = 0 6 + -18x + (7 * 7x + -1x * 7x) = 0 6 + -18x + (49x + -7x2) = 0 Combine like terms: -18x + 49x = 31x 6 + 31x + -7x2 = 0 Solving 6 + 31x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.8571428571 + -4.428571429x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -4.428571429x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -4.428571429x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -4.428571429x + x2 = 0 + 0.8571428571 -4.428571429x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -4.428571429x + x2 = 0.8571428571 The x term is -4.428571429x. Take half its coefficient (-2.214285715). Square it (4.903061228) and add it to both sides. Add '4.903061228' to each side of the equation. -4.428571429x + 4.903061228 + x2 = 0.8571428571 + 4.903061228 Reorder the terms: 4.903061228 + -4.428571429x + x2 = 0.8571428571 + 4.903061228 Combine like terms: 0.8571428571 + 4.903061228 = 5.7602040851 4.903061228 + -4.428571429x + x2 = 5.7602040851 Factor a perfect square on the left side: (x + -2.214285715)(x + -2.214285715) = 5.7602040851 Calculate the square root of the right side: 2.400042517 Break this problem into two subproblems by setting (x + -2.214285715) equal to 2.400042517 and -2.400042517.Subproblem 1
x + -2.214285715 = 2.400042517 Simplifying x + -2.214285715 = 2.400042517 Reorder the terms: -2.214285715 + x = 2.400042517 Solving -2.214285715 + x = 2.400042517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.214285715' to each side of the equation. -2.214285715 + 2.214285715 + x = 2.400042517 + 2.214285715 Combine like terms: -2.214285715 + 2.214285715 = 0.000000000 0.000000000 + x = 2.400042517 + 2.214285715 x = 2.400042517 + 2.214285715 Combine like terms: 2.400042517 + 2.214285715 = 4.614328232 x = 4.614328232 Simplifying x = 4.614328232Subproblem 2
x + -2.214285715 = -2.400042517 Simplifying x + -2.214285715 = -2.400042517 Reorder the terms: -2.214285715 + x = -2.400042517 Solving -2.214285715 + x = -2.400042517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.214285715' to each side of the equation. -2.214285715 + 2.214285715 + x = -2.400042517 + 2.214285715 Combine like terms: -2.214285715 + 2.214285715 = 0.000000000 0.000000000 + x = -2.400042517 + 2.214285715 x = -2.400042517 + 2.214285715 Combine like terms: -2.400042517 + 2.214285715 = -0.185756802 x = -0.185756802 Simplifying x = -0.185756802Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.614328232, -0.185756802}
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