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Simplifying -3a2 + 6a + -20 = -8a2 Reorder the terms: -20 + 6a + -3a2 = -8a2 Solving -20 + 6a + -3a2 = -8a2 Solving for variable 'a'. Combine like terms: -3a2 + 8a2 = 5a2 -20 + 6a + 5a2 = -8a2 + 8a2 Combine like terms: -8a2 + 8a2 = 0 -20 + 6a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 1.2a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.2a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + 1.2a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.2a + a2 = 0 + 4 1.2a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.2a + a2 = 4 The a term is 1.2a. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2a + 0.36 + a2 = 4 + 0.36 Reorder the terms: 0.36 + 1.2a + a2 = 4 + 0.36 Combine like terms: 4 + 0.36 = 4.36 0.36 + 1.2a + a2 = 4.36 Factor a perfect square on the left side: (a + 0.6)(a + 0.6) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (a + 0.6) equal to 2.088061302 and -2.088061302.Subproblem 1
a + 0.6 = 2.088061302 Simplifying a + 0.6 = 2.088061302 Reorder the terms: 0.6 + a = 2.088061302 Solving 0.6 + a = 2.088061302 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + a = 2.088061302 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + a = 2.088061302 + -0.6 a = 2.088061302 + -0.6 Combine like terms: 2.088061302 + -0.6 = 1.488061302 a = 1.488061302 Simplifying a = 1.488061302Subproblem 2
a + 0.6 = -2.088061302 Simplifying a + 0.6 = -2.088061302 Reorder the terms: 0.6 + a = -2.088061302 Solving 0.6 + a = -2.088061302 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + a = -2.088061302 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + a = -2.088061302 + -0.6 a = -2.088061302 + -0.6 Combine like terms: -2.088061302 + -0.6 = -2.688061302 a = -2.688061302 Simplifying a = -2.688061302Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.488061302, -2.688061302}
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