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Simplifying 4a2 + 5a + -8 = 0 Reorder the terms: -8 + 5a + 4a2 = 0 Solving -8 + 5a + 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'. -2 + 1.25a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.25a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 1.25a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.25a + a2 = 0 + 2 1.25a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.25a + a2 = 2 The a term is 1.25a. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25a + 0.390625 + a2 = 2 + 0.390625 Reorder the terms: 0.390625 + 1.25a + a2 = 2 + 0.390625 Combine like terms: 2 + 0.390625 = 2.390625 0.390625 + 1.25a + a2 = 2.390625 Factor a perfect square on the left side: (a + 0.625)(a + 0.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (a + 0.625) equal to 1.54616461 and -1.54616461.Subproblem 1
a + 0.625 = 1.54616461 Simplifying a + 0.625 = 1.54616461 Reorder the terms: 0.625 + a = 1.54616461 Solving 0.625 + a = 1.54616461 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + a = 1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + a = 1.54616461 + -0.625 a = 1.54616461 + -0.625 Combine like terms: 1.54616461 + -0.625 = 0.92116461 a = 0.92116461 Simplifying a = 0.92116461Subproblem 2
a + 0.625 = -1.54616461 Simplifying a + 0.625 = -1.54616461 Reorder the terms: 0.625 + a = -1.54616461 Solving 0.625 + a = -1.54616461 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + a = -1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + a = -1.54616461 + -0.625 a = -1.54616461 + -0.625 Combine like terms: -1.54616461 + -0.625 = -2.17116461 a = -2.17116461 Simplifying a = -2.17116461Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.92116461, -2.17116461}
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