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Simplifying 7x2 + 38x + 6 = 0 Reorder the terms: 6 + 38x + 7x2 = 0 Solving 6 + 38x + 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 + 5.428571429x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 5.428571429x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 5.428571429x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 5.428571429x + x2 = 0 + -0.8571428571 5.428571429x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 5.428571429x + x2 = -0.8571428571 The x term is 5.428571429x. Take half its coefficient (2.714285715). Square it (7.367346943) and add it to both sides. Add '7.367346943' to each side of the equation. 5.428571429x + 7.367346943 + x2 = -0.8571428571 + 7.367346943 Reorder the terms: 7.367346943 + 5.428571429x + x2 = -0.8571428571 + 7.367346943 Combine like terms: -0.8571428571 + 7.367346943 = 6.5102040859 7.367346943 + 5.428571429x + x2 = 6.5102040859 Factor a perfect square on the left side: (x + 2.714285715)(x + 2.714285715) = 6.5102040859 Calculate the square root of the right side: 2.551510158 Break this problem into two subproblems by setting (x + 2.714285715) equal to 2.551510158 and -2.551510158.Subproblem 1
x + 2.714285715 = 2.551510158 Simplifying x + 2.714285715 = 2.551510158 Reorder the terms: 2.714285715 + x = 2.551510158 Solving 2.714285715 + x = 2.551510158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.714285715' to each side of the equation. 2.714285715 + -2.714285715 + x = 2.551510158 + -2.714285715 Combine like terms: 2.714285715 + -2.714285715 = 0.000000000 0.000000000 + x = 2.551510158 + -2.714285715 x = 2.551510158 + -2.714285715 Combine like terms: 2.551510158 + -2.714285715 = -0.162775557 x = -0.162775557 Simplifying x = -0.162775557Subproblem 2
x + 2.714285715 = -2.551510158 Simplifying x + 2.714285715 = -2.551510158 Reorder the terms: 2.714285715 + x = -2.551510158 Solving 2.714285715 + x = -2.551510158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.714285715' to each side of the equation. 2.714285715 + -2.714285715 + x = -2.551510158 + -2.714285715 Combine like terms: 2.714285715 + -2.714285715 = 0.000000000 0.000000000 + x = -2.551510158 + -2.714285715 x = -2.551510158 + -2.714285715 Combine like terms: -2.551510158 + -2.714285715 = -5.265795873 x = -5.265795873 Simplifying x = -5.265795873Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.162775557, -5.265795873}
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