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Simplifying 4a2 + 40a + 5 = 0 Reorder the terms: 5 + 40a + 4a2 = 0 Solving 5 + 40a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 10a + a2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 10a + -1.25 + a2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 10a + a2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 10a + a2 = 0 + -1.25 10a + a2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 10a + a2 = -1.25 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 = -1.25 + 25 Reorder the terms: 25 + 10a + a2 = -1.25 + 25 Combine like terms: -1.25 + 25 = 23.75 25 + 10a + a2 = 23.75 Factor a perfect square on the left side: (a + 5)(a + 5) = 23.75 Calculate the square root of the right side: 4.873397172 Break this problem into two subproblems by setting (a + 5) equal to 4.873397172 and -4.873397172.Subproblem 1
a + 5 = 4.873397172 Simplifying a + 5 = 4.873397172 Reorder the terms: 5 + a = 4.873397172 Solving 5 + a = 4.873397172 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 = 4.873397172 + -5 Combine like terms: 5 + -5 = 0 0 + a = 4.873397172 + -5 a = 4.873397172 + -5 Combine like terms: 4.873397172 + -5 = -0.126602828 a = -0.126602828 Simplifying a = -0.126602828Subproblem 2
a + 5 = -4.873397172 Simplifying a + 5 = -4.873397172 Reorder the terms: 5 + a = -4.873397172 Solving 5 + a = -4.873397172 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 = -4.873397172 + -5 Combine like terms: 5 + -5 = 0 0 + a = -4.873397172 + -5 a = -4.873397172 + -5 Combine like terms: -4.873397172 + -5 = -9.873397172 a = -9.873397172 Simplifying a = -9.873397172Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.126602828, -9.873397172}
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