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Simplifying 3a2 + 6a + -18 = 5 Reorder the terms: -18 + 6a + 3a2 = 5 Solving -18 + 6a + 3a2 = 5 Solving for variable 'a'. Reorder the terms: -18 + -5 + 6a + 3a2 = 5 + -5 Combine like terms: -18 + -5 = -23 -23 + 6a + 3a2 = 5 + -5 Combine like terms: 5 + -5 = 0 -23 + 6a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.666666667 + 2a + a2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + 2a + 7.666666667 + a2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + 2a + a2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + 2a + a2 = 0 + 7.666666667 2a + a2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 2a + a2 = 7.666666667 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 7.666666667 + 1 Reorder the terms: 1 + 2a + a2 = 7.666666667 + 1 Combine like terms: 7.666666667 + 1 = 8.666666667 1 + 2a + a2 = 8.666666667 Factor a perfect square on the left side: (a + 1)(a + 1) = 8.666666667 Calculate the square root of the right side: 2.943920289 Break this problem into two subproblems by setting (a + 1) equal to 2.943920289 and -2.943920289.Subproblem 1
a + 1 = 2.943920289 Simplifying a + 1 = 2.943920289 Reorder the terms: 1 + a = 2.943920289 Solving 1 + a = 2.943920289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 2.943920289 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.943920289 + -1 a = 2.943920289 + -1 Combine like terms: 2.943920289 + -1 = 1.943920289 a = 1.943920289 Simplifying a = 1.943920289Subproblem 2
a + 1 = -2.943920289 Simplifying a + 1 = -2.943920289 Reorder the terms: 1 + a = -2.943920289 Solving 1 + a = -2.943920289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -2.943920289 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.943920289 + -1 a = -2.943920289 + -1 Combine like terms: -2.943920289 + -1 = -3.943920289 a = -3.943920289 Simplifying a = -3.943920289Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.943920289, -3.943920289}
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