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Simplifying (-7a2 + 7a + -2) + (8a2 + -2a + -3) = 0 Reorder the terms: (-2 + 7a + -7a2) + (8a2 + -2a + -3) = 0 Remove parenthesis around (-2 + 7a + -7a2) -2 + 7a + -7a2 + (8a2 + -2a + -3) = 0 Reorder the terms: -2 + 7a + -7a2 + (-3 + -2a + 8a2) = 0 Remove parenthesis around (-3 + -2a + 8a2) -2 + 7a + -7a2 + -3 + -2a + 8a2 = 0 Reorder the terms: -2 + -3 + 7a + -2a + -7a2 + 8a2 = 0 Combine like terms: -2 + -3 = -5 -5 + 7a + -2a + -7a2 + 8a2 = 0 Combine like terms: 7a + -2a = 5a -5 + 5a + -7a2 + 8a2 = 0 Combine like terms: -7a2 + 8a2 = 1a2 -5 + 5a + 1a2 = 0 Solving -5 + 5a + 1a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 5a + 5 + a2 = 0 + 5 Reorder the terms: -5 + 5 + 5a + a2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5a + a2 = 0 + 5 5a + a2 = 0 + 5 Combine like terms: 0 + 5 = 5 5a + a2 = 5 The a term is 5a. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5a + 6.25 + a2 = 5 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 5 + 6.25 Combine like terms: 5 + 6.25 = 11.25 6.25 + 5a + a2 = 11.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (a + 2.5) equal to 3.354101966 and -3.354101966.Subproblem 1
a + 2.5 = 3.354101966 Simplifying a + 2.5 = 3.354101966 Reorder the terms: 2.5 + a = 3.354101966 Solving 2.5 + a = 3.354101966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 3.354101966 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 3.354101966 + -2.5 a = 3.354101966 + -2.5 Combine like terms: 3.354101966 + -2.5 = 0.854101966 a = 0.854101966 Simplifying a = 0.854101966Subproblem 2
a + 2.5 = -3.354101966 Simplifying a + 2.5 = -3.354101966 Reorder the terms: 2.5 + a = -3.354101966 Solving 2.5 + a = -3.354101966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -3.354101966 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -3.354101966 + -2.5 a = -3.354101966 + -2.5 Combine like terms: -3.354101966 + -2.5 = -5.854101966 a = -5.854101966 Simplifying a = -5.854101966Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.854101966, -5.854101966}
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