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Simplifying 0.2a2 + 2a + 2.5 = 0 Reorder the terms: 2.5 + 2a + 0.2a2 = 0 Solving 2.5 + 2a + 0.2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 12.5 + 10a + a2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 10a + -12.5 + a2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 10a + a2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 10a + a2 = 0 + -12.5 10a + a2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 10a + a2 = -12.5 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = -12.5 + 25 Reorder the terms: 25 + 10a + a2 = -12.5 + 25 Combine like terms: -12.5 + 25 = 12.5 25 + 10a + a2 = 12.5 Factor a perfect square on the left side: (a + 5)(a + 5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (a + 5) equal to 3.535533906 and -3.535533906.Subproblem 1
a + 5 = 3.535533906 Simplifying a + 5 = 3.535533906 Reorder the terms: 5 + a = 3.535533906 Solving 5 + a = 3.535533906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 3.535533906 + -5 Combine like terms: 5 + -5 = 0 0 + a = 3.535533906 + -5 a = 3.535533906 + -5 Combine like terms: 3.535533906 + -5 = -1.464466094 a = -1.464466094 Simplifying a = -1.464466094Subproblem 2
a + 5 = -3.535533906 Simplifying a + 5 = -3.535533906 Reorder the terms: 5 + a = -3.535533906 Solving 5 + a = -3.535533906 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -3.535533906 + -5 Combine like terms: 5 + -5 = 0 0 + a = -3.535533906 + -5 a = -3.535533906 + -5 Combine like terms: -3.535533906 + -5 = -8.535533906 a = -8.535533906 Simplifying a = -8.535533906Solution
The solution to the problem is based on the solutions from the subproblems. a = {-1.464466094, -8.535533906}
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