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Simplifying 2a2 + -11a = 12 Reorder the terms: -11a + 2a2 = 12 Solving -11a + 2a2 = 12 Solving for variable 'a'. Reorder the terms: -12 + -11a + 2a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -11a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -5.5a + a2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -5.5a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + -5.5a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5.5a + a2 = 0 + 6 -5.5a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5.5a + a2 = 6 The a term is -5.5a. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5a + 7.5625 + a2 = 6 + 7.5625 Reorder the terms: 7.5625 + -5.5a + a2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + -5.5a + a2 = 13.5625 Factor a perfect square on the left side: (a + -2.75)(a + -2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (a + -2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
a + -2.75 = 3.682729966 Simplifying a + -2.75 = 3.682729966 Reorder the terms: -2.75 + a = 3.682729966 Solving -2.75 + a = 3.682729966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = 3.682729966 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = 3.682729966 + 2.75 a = 3.682729966 + 2.75 Combine like terms: 3.682729966 + 2.75 = 6.432729966 a = 6.432729966 Simplifying a = 6.432729966Subproblem 2
a + -2.75 = -3.682729966 Simplifying a + -2.75 = -3.682729966 Reorder the terms: -2.75 + a = -3.682729966 Solving -2.75 + a = -3.682729966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = -3.682729966 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = -3.682729966 + 2.75 a = -3.682729966 + 2.75 Combine like terms: -3.682729966 + 2.75 = -0.932729966 a = -0.932729966 Simplifying a = -0.932729966Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.432729966, -0.932729966}
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