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Simplifying -3 + 4a + 5a2 = 0 Solving -3 + 4a + 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 + 0.8a + a2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.8a + 0.6 + a2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.8a + a2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.8a + a2 = 0 + 0.6 0.8a + a2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.8a + a2 = 0.6 The a term is 0.8a. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8a + 0.16 + a2 = 0.6 + 0.16 Reorder the terms: 0.16 + 0.8a + a2 = 0.6 + 0.16 Combine like terms: 0.6 + 0.16 = 0.76 0.16 + 0.8a + a2 = 0.76 Factor a perfect square on the left side: (a + 0.4)(a + 0.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (a + 0.4) equal to 0.871779789 and -0.871779789.Subproblem 1
a + 0.4 = 0.871779789 Simplifying a + 0.4 = 0.871779789 Reorder the terms: 0.4 + a = 0.871779789 Solving 0.4 + a = 0.871779789 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + a = 0.871779789 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + a = 0.871779789 + -0.4 a = 0.871779789 + -0.4 Combine like terms: 0.871779789 + -0.4 = 0.471779789 a = 0.471779789 Simplifying a = 0.471779789Subproblem 2
a + 0.4 = -0.871779789 Simplifying a + 0.4 = -0.871779789 Reorder the terms: 0.4 + a = -0.871779789 Solving 0.4 + a = -0.871779789 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + a = -0.871779789 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + a = -0.871779789 + -0.4 a = -0.871779789 + -0.4 Combine like terms: -0.871779789 + -0.4 = -1.271779789 a = -1.271779789 Simplifying a = -1.271779789Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.471779789, -1.271779789}
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