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Simplifying -5a + 57 = 2a2 + -9 Reorder the terms: 57 + -5a = 2a2 + -9 Reorder the terms: 57 + -5a = -9 + 2a2 Solving 57 + -5a = -9 + 2a2 Solving for variable 'a'. Reorder the terms: 57 + 9 + -5a + -2a2 = -9 + 2a2 + 9 + -2a2 Combine like terms: 57 + 9 = 66 66 + -5a + -2a2 = -9 + 2a2 + 9 + -2a2 Reorder the terms: 66 + -5a + -2a2 = -9 + 9 + 2a2 + -2a2 Combine like terms: -9 + 9 = 0 66 + -5a + -2a2 = 0 + 2a2 + -2a2 66 + -5a + -2a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 66 + -5a + -2a2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -33 + 2.5a + a2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 2.5a + 33 + a2 = 0 + 33 Reorder the terms: -33 + 33 + 2.5a + a2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 2.5a + a2 = 0 + 33 2.5a + a2 = 0 + 33 Combine like terms: 0 + 33 = 33 2.5a + a2 = 33 The a term is 2.5a. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5a + 1.5625 + a2 = 33 + 1.5625 Reorder the terms: 1.5625 + 2.5a + a2 = 33 + 1.5625 Combine like terms: 33 + 1.5625 = 34.5625 1.5625 + 2.5a + a2 = 34.5625 Factor a perfect square on the left side: (a + 1.25)(a + 1.25) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (a + 1.25) equal to 5.878988008 and -5.878988008.Subproblem 1
a + 1.25 = 5.878988008 Simplifying a + 1.25 = 5.878988008 Reorder the terms: 1.25 + a = 5.878988008 Solving 1.25 + a = 5.878988008 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a = 5.878988008 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a = 5.878988008 + -1.25 a = 5.878988008 + -1.25 Combine like terms: 5.878988008 + -1.25 = 4.628988008 a = 4.628988008 Simplifying a = 4.628988008Subproblem 2
a + 1.25 = -5.878988008 Simplifying a + 1.25 = -5.878988008 Reorder the terms: 1.25 + a = -5.878988008 Solving 1.25 + a = -5.878988008 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + a = -5.878988008 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + a = -5.878988008 + -1.25 a = -5.878988008 + -1.25 Combine like terms: -5.878988008 + -1.25 = -7.128988008 a = -7.128988008 Simplifying a = -7.128988008Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.628988008, -7.128988008}
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