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Simplifying 2.8a + 5a2 + -5 = 0 Reorder the terms: -5 + 2.8a + 5a2 = 0 Solving -5 + 2.8a + 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'. -1 + 0.56a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.56a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 0.56a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.56a + a2 = 0 + 1 0.56a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.56a + a2 = 1 The a term is 0.56a. Take half its coefficient (0.28). Square it (0.0784) and add it to both sides. Add '0.0784' to each side of the equation. 0.56a + 0.0784 + a2 = 1 + 0.0784 Reorder the terms: 0.0784 + 0.56a + a2 = 1 + 0.0784 Combine like terms: 1 + 0.0784 = 1.0784 0.0784 + 0.56a + a2 = 1.0784 Factor a perfect square on the left side: (a + 0.28)(a + 0.28) = 1.0784 Calculate the square root of the right side: 1.038460399 Break this problem into two subproblems by setting (a + 0.28) equal to 1.038460399 and -1.038460399.Subproblem 1
a + 0.28 = 1.038460399 Simplifying a + 0.28 = 1.038460399 Reorder the terms: 0.28 + a = 1.038460399 Solving 0.28 + a = 1.038460399 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.28' to each side of the equation. 0.28 + -0.28 + a = 1.038460399 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 0.00 + a = 1.038460399 + -0.28 a = 1.038460399 + -0.28 Combine like terms: 1.038460399 + -0.28 = 0.758460399 a = 0.758460399 Simplifying a = 0.758460399Subproblem 2
a + 0.28 = -1.038460399 Simplifying a + 0.28 = -1.038460399 Reorder the terms: 0.28 + a = -1.038460399 Solving 0.28 + a = -1.038460399 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.28' to each side of the equation. 0.28 + -0.28 + a = -1.038460399 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 0.00 + a = -1.038460399 + -0.28 a = -1.038460399 + -0.28 Combine like terms: -1.038460399 + -0.28 = -1.318460399 a = -1.318460399 Simplifying a = -1.318460399Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.758460399, -1.318460399}
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