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Simplifying 5a2 + 20a + 3 = 0 Reorder the terms: 3 + 20a + 5a2 = 0 Solving 3 + 20a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 4a + a2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 4a + -0.6 + a2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 4a + a2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 4a + a2 = 0 + -0.6 4a + a2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 4a + a2 = -0.6 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = -0.6 + 4 Reorder the terms: 4 + 4a + a2 = -0.6 + 4 Combine like terms: -0.6 + 4 = 3.4 4 + 4a + a2 = 3.4 Factor a perfect square on the left side: (a + 2)(a + 2) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (a + 2) equal to 1.843908891 and -1.843908891.Subproblem 1
a + 2 = 1.843908891 Simplifying a + 2 = 1.843908891 Reorder the terms: 2 + a = 1.843908891 Solving 2 + a = 1.843908891 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 1.843908891 + -2 Combine like terms: 2 + -2 = 0 0 + a = 1.843908891 + -2 a = 1.843908891 + -2 Combine like terms: 1.843908891 + -2 = -0.156091109 a = -0.156091109 Simplifying a = -0.156091109Subproblem 2
a + 2 = -1.843908891 Simplifying a + 2 = -1.843908891 Reorder the terms: 2 + a = -1.843908891 Solving 2 + a = -1.843908891 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -1.843908891 + -2 Combine like terms: 2 + -2 = 0 0 + a = -1.843908891 + -2 a = -1.843908891 + -2 Combine like terms: -1.843908891 + -2 = -3.843908891 a = -3.843908891 Simplifying a = -3.843908891Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.156091109, -3.843908891}
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