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Simplifying 7x2 + 8x + -1 = 0 Reorder the terms: -1 + 8x + 7x2 = 0 Solving -1 + 8x + 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'. -0.1428571429 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 1.142857143x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 1.142857143x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 1.142857143x + x2 = 0 + 0.1428571429 1.142857143x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 1.142857143x + x2 = 0.1428571429 The x term is 1.142857143x. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143x + 0.3265306123 + x2 = 0.1428571429 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 0.1428571429 + 0.3265306123 Combine like terms: 0.1428571429 + 0.3265306123 = 0.4693877552 0.3265306123 + 1.142857143x + x2 = 0.4693877552 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 0.4693877552 Calculate the square root of the right side: 0.685118789 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 0.685118789 and -0.685118789.Subproblem 1
x + 0.5714285715 = 0.685118789 Simplifying x + 0.5714285715 = 0.685118789 Reorder the terms: 0.5714285715 + x = 0.685118789 Solving 0.5714285715 + x = 0.685118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = 0.685118789 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 0.685118789 + -0.5714285715 x = 0.685118789 + -0.5714285715 Combine like terms: 0.685118789 + -0.5714285715 = 0.1136902175 x = 0.1136902175 Simplifying x = 0.1136902175Subproblem 2
x + 0.5714285715 = -0.685118789 Simplifying x + 0.5714285715 = -0.685118789 Reorder the terms: 0.5714285715 + x = -0.685118789 Solving 0.5714285715 + x = -0.685118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + x = -0.685118789 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -0.685118789 + -0.5714285715 x = -0.685118789 + -0.5714285715 Combine like terms: -0.685118789 + -0.5714285715 = -1.2565473605 x = -1.2565473605 Simplifying x = -1.2565473605Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1136902175, -1.2565473605}
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