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Simplifying 14a2 + 9a + -207 = 0 Reorder the terms: -207 + 9a + 14a2 = 0 Solving -207 + 9a + 14a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -14.78571429 + 0.6428571429a + a2 = 0 Move the constant term to the right: Add '14.78571429' to each side of the equation. -14.78571429 + 0.6428571429a + 14.78571429 + a2 = 0 + 14.78571429 Reorder the terms: -14.78571429 + 14.78571429 + 0.6428571429a + a2 = 0 + 14.78571429 Combine like terms: -14.78571429 + 14.78571429 = 0.00000000 0.00000000 + 0.6428571429a + a2 = 0 + 14.78571429 0.6428571429a + a2 = 0 + 14.78571429 Combine like terms: 0 + 14.78571429 = 14.78571429 0.6428571429a + a2 = 14.78571429 The a term is 0.6428571429a. Take half its coefficient (0.3214285715). Square it (0.1033163266) and add it to both sides. Add '0.1033163266' to each side of the equation. 0.6428571429a + 0.1033163266 + a2 = 14.78571429 + 0.1033163266 Reorder the terms: 0.1033163266 + 0.6428571429a + a2 = 14.78571429 + 0.1033163266 Combine like terms: 14.78571429 + 0.1033163266 = 14.8890306166 0.1033163266 + 0.6428571429a + a2 = 14.8890306166 Factor a perfect square on the left side: (a + 0.3214285715)(a + 0.3214285715) = 14.8890306166 Calculate the square root of the right side: 3.858630666 Break this problem into two subproblems by setting (a + 0.3214285715) equal to 3.858630666 and -3.858630666.Subproblem 1
a + 0.3214285715 = 3.858630666 Simplifying a + 0.3214285715 = 3.858630666 Reorder the terms: 0.3214285715 + a = 3.858630666 Solving 0.3214285715 + a = 3.858630666 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3214285715' to each side of the equation. 0.3214285715 + -0.3214285715 + a = 3.858630666 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + a = 3.858630666 + -0.3214285715 a = 3.858630666 + -0.3214285715 Combine like terms: 3.858630666 + -0.3214285715 = 3.5372020945 a = 3.5372020945 Simplifying a = 3.5372020945Subproblem 2
a + 0.3214285715 = -3.858630666 Simplifying a + 0.3214285715 = -3.858630666 Reorder the terms: 0.3214285715 + a = -3.858630666 Solving 0.3214285715 + a = -3.858630666 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3214285715' to each side of the equation. 0.3214285715 + -0.3214285715 + a = -3.858630666 + -0.3214285715 Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000 0.0000000000 + a = -3.858630666 + -0.3214285715 a = -3.858630666 + -0.3214285715 Combine like terms: -3.858630666 + -0.3214285715 = -4.1800592375 a = -4.1800592375 Simplifying a = -4.1800592375Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.5372020945, -4.1800592375}
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