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Simplifying 20a2 + -13a + -12 = 0 Reorder the terms: -12 + -13a + 20a2 = 0 Solving -12 + -13a + 20a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.6 + -0.65a + a2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.65a + 0.6 + a2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.65a + a2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.65a + a2 = 0 + 0.6 -0.65a + a2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.65a + a2 = 0.6 The a term is -0.65a. Take half its coefficient (-0.325). Square it (0.105625) and add it to both sides. Add '0.105625' to each side of the equation. -0.65a + 0.105625 + a2 = 0.6 + 0.105625 Reorder the terms: 0.105625 + -0.65a + a2 = 0.6 + 0.105625 Combine like terms: 0.6 + 0.105625 = 0.705625 0.105625 + -0.65a + a2 = 0.705625 Factor a perfect square on the left side: (a + -0.325)(a + -0.325) = 0.705625 Calculate the square root of the right side: 0.840014881 Break this problem into two subproblems by setting (a + -0.325) equal to 0.840014881 and -0.840014881.Subproblem 1
a + -0.325 = 0.840014881 Simplifying a + -0.325 = 0.840014881 Reorder the terms: -0.325 + a = 0.840014881 Solving -0.325 + a = 0.840014881 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + a = 0.840014881 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + a = 0.840014881 + 0.325 a = 0.840014881 + 0.325 Combine like terms: 0.840014881 + 0.325 = 1.165014881 a = 1.165014881 Simplifying a = 1.165014881Subproblem 2
a + -0.325 = -0.840014881 Simplifying a + -0.325 = -0.840014881 Reorder the terms: -0.325 + a = -0.840014881 Solving -0.325 + a = -0.840014881 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.325' to each side of the equation. -0.325 + 0.325 + a = -0.840014881 + 0.325 Combine like terms: -0.325 + 0.325 = 0.000 0.000 + a = -0.840014881 + 0.325 a = -0.840014881 + 0.325 Combine like terms: -0.840014881 + 0.325 = -0.515014881 a = -0.515014881 Simplifying a = -0.515014881Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.165014881, -0.515014881}
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