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Simplifying 3a2 + 13a + -39 = 0 Reorder the terms: -39 + 13a + 3a2 = 0 Solving -39 + 13a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13 + 4.333333333a + a2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 4.333333333a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + 4.333333333a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4.333333333a + a2 = 0 + 13 4.333333333a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 4.333333333a + a2 = 13 The a term is 4.333333333a. Take half its coefficient (2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. 4.333333333a + 4.694444446 + a2 = 13 + 4.694444446 Reorder the terms: 4.694444446 + 4.333333333a + a2 = 13 + 4.694444446 Combine like terms: 13 + 4.694444446 = 17.694444446 4.694444446 + 4.333333333a + a2 = 17.694444446 Factor a perfect square on the left side: (a + 2.166666667)(a + 2.166666667) = 17.694444446 Calculate the square root of the right side: 4.206476488 Break this problem into two subproblems by setting (a + 2.166666667) equal to 4.206476488 and -4.206476488.Subproblem 1
a + 2.166666667 = 4.206476488 Simplifying a + 2.166666667 = 4.206476488 Reorder the terms: 2.166666667 + a = 4.206476488 Solving 2.166666667 + a = 4.206476488 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + a = 4.206476488 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + a = 4.206476488 + -2.166666667 a = 4.206476488 + -2.166666667 Combine like terms: 4.206476488 + -2.166666667 = 2.039809821 a = 2.039809821 Simplifying a = 2.039809821Subproblem 2
a + 2.166666667 = -4.206476488 Simplifying a + 2.166666667 = -4.206476488 Reorder the terms: 2.166666667 + a = -4.206476488 Solving 2.166666667 + a = -4.206476488 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + a = -4.206476488 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + a = -4.206476488 + -2.166666667 a = -4.206476488 + -2.166666667 Combine like terms: -4.206476488 + -2.166666667 = -6.373143155 a = -6.373143155 Simplifying a = -6.373143155Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.039809821, -6.373143155}
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