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Simplifying (2a2 + 3a + -7) + (-3a2 + 5a + 6) = 0 Reorder the terms: (-7 + 3a + 2a2) + (-3a2 + 5a + 6) = 0 Remove parenthesis around (-7 + 3a + 2a2) -7 + 3a + 2a2 + (-3a2 + 5a + 6) = 0 Reorder the terms: -7 + 3a + 2a2 + (6 + 5a + -3a2) = 0 Remove parenthesis around (6 + 5a + -3a2) -7 + 3a + 2a2 + 6 + 5a + -3a2 = 0 Reorder the terms: -7 + 6 + 3a + 5a + 2a2 + -3a2 = 0 Combine like terms: -7 + 6 = -1 -1 + 3a + 5a + 2a2 + -3a2 = 0 Combine like terms: 3a + 5a = 8a -1 + 8a + 2a2 + -3a2 = 0 Combine like terms: 2a2 + -3a2 = -1a2 -1 + 8a + -1a2 = 0 Solving -1 + 8a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -8a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -8a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8a + a2 = 0 + -1 -8a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8a + a2 = -1 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = -1 + 16 Reorder the terms: 16 + -8a + a2 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + -8a + a2 = 15 Factor a perfect square on the left side: (a + -4)(a + -4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (a + -4) equal to 3.872983346 and -3.872983346.Subproblem 1
a + -4 = 3.872983346 Simplifying a + -4 = 3.872983346 Reorder the terms: -4 + a = 3.872983346 Solving -4 + a = 3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + a = 3.872983346 + 4 a = 3.872983346 + 4 Combine like terms: 3.872983346 + 4 = 7.872983346 a = 7.872983346 Simplifying a = 7.872983346Subproblem 2
a + -4 = -3.872983346 Simplifying a + -4 = -3.872983346 Reorder the terms: -4 + a = -3.872983346 Solving -4 + a = -3.872983346 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -3.872983346 + 4 Combine like terms: -4 + 4 = 0 0 + a = -3.872983346 + 4 a = -3.872983346 + 4 Combine like terms: -3.872983346 + 4 = 0.127016654 a = 0.127016654 Simplifying a = 0.127016654Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.872983346, 0.127016654}
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