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Simplifying 3a2 + -5 + 2a + -4(6 + -2a) + 7a2 = 0 3a2 + -5 + 2a + (6 * -4 + -2a * -4) + 7a2 = 0 3a2 + -5 + 2a + (-24 + 8a) + 7a2 = 0 Reorder the terms: -5 + -24 + 2a + 8a + 3a2 + 7a2 = 0 Combine like terms: -5 + -24 = -29 -29 + 2a + 8a + 3a2 + 7a2 = 0 Combine like terms: 2a + 8a = 10a -29 + 10a + 3a2 + 7a2 = 0 Combine like terms: 3a2 + 7a2 = 10a2 -29 + 10a + 10a2 = 0 Solving -29 + 10a + 10a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.9 + a + a2 = 0.0 Move the constant term to the right: Add '2.9' to each side of the equation. -2.9 + a + 2.9 + a2 = 0.0 + 2.9 Reorder the terms: -2.9 + 2.9 + a + a2 = 0.0 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + a + a2 = 0.0 + 2.9 a + a2 = 0.0 + 2.9 Combine like terms: 0.0 + 2.9 = 2.9 a + a2 = 2.9 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 2.9 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 2.9 + 0.25 Combine like terms: 2.9 + 0.25 = 3.15 1.25 + a2 = 3.15 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 3.15 Calculate the square root of the right side: 1.774823935 Break this problem into two subproblems by setting (a + 0.5) equal to 1.774823935 and -1.774823935.Subproblem 1
a + 0.5 = 1.774823935 Simplifying a + 0.5 = 1.774823935 Reorder the terms: 0.5 + a = 1.774823935 Solving 0.5 + a = 1.774823935 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 1.774823935 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 1.774823935 + -0.5 a = 1.774823935 + -0.5 Combine like terms: 1.774823935 + -0.5 = 1.274823935 a = 1.274823935 Simplifying a = 1.274823935Subproblem 2
a + 0.5 = -1.774823935 Simplifying a + 0.5 = -1.774823935 Reorder the terms: 0.5 + a = -1.774823935 Solving 0.5 + a = -1.774823935 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -1.774823935 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -1.774823935 + -0.5 a = -1.774823935 + -0.5 Combine like terms: -1.774823935 + -0.5 = -2.274823935 a = -2.274823935 Simplifying a = -2.274823935Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.274823935, -2.274823935}
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