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Simplifying 7x2 + 8x + -65 = 0 Reorder the terms: -65 + 8x + 7x2 = 0 Solving -65 + 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'. -9.285714286 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '9.285714286' to each side of the equation. -9.285714286 + 1.142857143x + 9.285714286 + x2 = 0 + 9.285714286 Reorder the terms: -9.285714286 + 9.285714286 + 1.142857143x + x2 = 0 + 9.285714286 Combine like terms: -9.285714286 + 9.285714286 = 0.000000000 0.000000000 + 1.142857143x + x2 = 0 + 9.285714286 1.142857143x + x2 = 0 + 9.285714286 Combine like terms: 0 + 9.285714286 = 9.285714286 1.142857143x + x2 = 9.285714286 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 = 9.285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 9.285714286 + 0.3265306123 Combine like terms: 9.285714286 + 0.3265306123 = 9.6122448983 0.3265306123 + 1.142857143x + x2 = 9.6122448983 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 9.6122448983 Calculate the square root of the right side: 3.100362059 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 3.100362059 and -3.100362059.Subproblem 1
x + 0.5714285715 = 3.100362059 Simplifying x + 0.5714285715 = 3.100362059 Reorder the terms: 0.5714285715 + x = 3.100362059 Solving 0.5714285715 + x = 3.100362059 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 = 3.100362059 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 3.100362059 + -0.5714285715 x = 3.100362059 + -0.5714285715 Combine like terms: 3.100362059 + -0.5714285715 = 2.5289334875 x = 2.5289334875 Simplifying x = 2.5289334875Subproblem 2
x + 0.5714285715 = -3.100362059 Simplifying x + 0.5714285715 = -3.100362059 Reorder the terms: 0.5714285715 + x = -3.100362059 Solving 0.5714285715 + x = -3.100362059 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 = -3.100362059 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -3.100362059 + -0.5714285715 x = -3.100362059 + -0.5714285715 Combine like terms: -3.100362059 + -0.5714285715 = -3.6717906305 x = -3.6717906305 Simplifying x = -3.6717906305Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5289334875, -3.6717906305}
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