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Simplifying 7a2 + 40a = 7 + -40a Reorder the terms: 40a + 7a2 = 7 + -40a Solving 40a + 7a2 = 7 + -40a Solving for variable 'a'. Reorder the terms: -7 + 40a + 40a + 7a2 = 7 + -40a + -7 + 40a Combine like terms: 40a + 40a = 80a -7 + 80a + 7a2 = 7 + -40a + -7 + 40a Reorder the terms: -7 + 80a + 7a2 = 7 + -7 + -40a + 40a Combine like terms: 7 + -7 = 0 -7 + 80a + 7a2 = 0 + -40a + 40a -7 + 80a + 7a2 = -40a + 40a Combine like terms: -40a + 40a = 0 -7 + 80a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 11.42857143a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 11.42857143a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 11.42857143a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 11.42857143a + a2 = 0 + 1 11.42857143a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 11.42857143a + a2 = 1 The a term is 11.42857143a. Take half its coefficient (5.714285715). Square it (32.65306123) and add it to both sides. Add '32.65306123' to each side of the equation. 11.42857143a + 32.65306123 + a2 = 1 + 32.65306123 Reorder the terms: 32.65306123 + 11.42857143a + a2 = 1 + 32.65306123 Combine like terms: 1 + 32.65306123 = 33.65306123 32.65306123 + 11.42857143a + a2 = 33.65306123 Factor a perfect square on the left side: (a + 5.714285715)(a + 5.714285715) = 33.65306123 Calculate the square root of the right side: 5.801125859 Break this problem into two subproblems by setting (a + 5.714285715) equal to 5.801125859 and -5.801125859.Subproblem 1
a + 5.714285715 = 5.801125859 Simplifying a + 5.714285715 = 5.801125859 Reorder the terms: 5.714285715 + a = 5.801125859 Solving 5.714285715 + a = 5.801125859 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.714285715' to each side of the equation. 5.714285715 + -5.714285715 + a = 5.801125859 + -5.714285715 Combine like terms: 5.714285715 + -5.714285715 = 0.000000000 0.000000000 + a = 5.801125859 + -5.714285715 a = 5.801125859 + -5.714285715 Combine like terms: 5.801125859 + -5.714285715 = 0.086840144 a = 0.086840144 Simplifying a = 0.086840144Subproblem 2
a + 5.714285715 = -5.801125859 Simplifying a + 5.714285715 = -5.801125859 Reorder the terms: 5.714285715 + a = -5.801125859 Solving 5.714285715 + a = -5.801125859 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.714285715' to each side of the equation. 5.714285715 + -5.714285715 + a = -5.801125859 + -5.714285715 Combine like terms: 5.714285715 + -5.714285715 = 0.000000000 0.000000000 + a = -5.801125859 + -5.714285715 a = -5.801125859 + -5.714285715 Combine like terms: -5.801125859 + -5.714285715 = -11.515411574 a = -11.515411574 Simplifying a = -11.515411574Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.086840144, -11.515411574}
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