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Simplifying 7a2 + -16 = 8a Reorder the terms: -16 + 7a2 = 8a Solving -16 + 7a2 = 8a Solving for variable 'a'. Reorder the terms: -16 + -8a + 7a2 = 8a + -8a Combine like terms: 8a + -8a = 0 -16 + -8a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + -1.142857143a + a2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -1.142857143a + 2.285714286 + a2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -1.142857143a + a2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -1.142857143a + a2 = 0 + 2.285714286 -1.142857143a + a2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -1.142857143a + a2 = 2.285714286 The a term is -1.142857143a. 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. -1.142857143a + 0.3265306123 + a2 = 2.285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143a + a2 = 2.285714286 + 0.3265306123 Combine like terms: 2.285714286 + 0.3265306123 = 2.6122448983 0.3265306123 + -1.142857143a + a2 = 2.6122448983 Factor a perfect square on the left side: (a + -0.5714285715)(a + -0.5714285715) = 2.6122448983 Calculate the square root of the right side: 1.616244071 Break this problem into two subproblems by setting (a + -0.5714285715) equal to 1.616244071 and -1.616244071.Subproblem 1
a + -0.5714285715 = 1.616244071 Simplifying a + -0.5714285715 = 1.616244071 Reorder the terms: -0.5714285715 + a = 1.616244071 Solving -0.5714285715 + a = 1.616244071 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + a = 1.616244071 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + a = 1.616244071 + 0.5714285715 a = 1.616244071 + 0.5714285715 Combine like terms: 1.616244071 + 0.5714285715 = 2.1876726425 a = 2.1876726425 Simplifying a = 2.1876726425Subproblem 2
a + -0.5714285715 = -1.616244071 Simplifying a + -0.5714285715 = -1.616244071 Reorder the terms: -0.5714285715 + a = -1.616244071 Solving -0.5714285715 + a = -1.616244071 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + a = -1.616244071 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + a = -1.616244071 + 0.5714285715 a = -1.616244071 + 0.5714285715 Combine like terms: -1.616244071 + 0.5714285715 = -1.0448154995 a = -1.0448154995 Simplifying a = -1.0448154995Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.1876726425, -1.0448154995}
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