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Simplifying 3a2 + -30a + -80 = 0 Reorder the terms: -80 + -30a + 3a2 = 0 Solving -80 + -30a + 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'. -26.66666667 + -10a + a2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + -10a + 26.66666667 + a2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + -10a + a2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + -10a + a2 = 0 + 26.66666667 -10a + a2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 -10a + a2 = 26.66666667 The a term is -10a. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a + 25 + a2 = 26.66666667 + 25 Reorder the terms: 25 + -10a + a2 = 26.66666667 + 25 Combine like terms: 26.66666667 + 25 = 51.66666667 25 + -10a + a2 = 51.66666667 Factor a perfect square on the left side: (a + -5)(a + -5) = 51.66666667 Calculate the square root of the right side: 7.187952885 Break this problem into two subproblems by setting (a + -5) equal to 7.187952885 and -7.187952885.Subproblem 1
a + -5 = 7.187952885 Simplifying a + -5 = 7.187952885 Reorder the terms: -5 + a = 7.187952885 Solving -5 + a = 7.187952885 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 7.187952885 + 5 Combine like terms: -5 + 5 = 0 0 + a = 7.187952885 + 5 a = 7.187952885 + 5 Combine like terms: 7.187952885 + 5 = 12.187952885 a = 12.187952885 Simplifying a = 12.187952885Subproblem 2
a + -5 = -7.187952885 Simplifying a + -5 = -7.187952885 Reorder the terms: -5 + a = -7.187952885 Solving -5 + a = -7.187952885 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -7.187952885 + 5 Combine like terms: -5 + 5 = 0 0 + a = -7.187952885 + 5 a = -7.187952885 + 5 Combine like terms: -7.187952885 + 5 = -2.187952885 a = -2.187952885 Simplifying a = -2.187952885Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.187952885, -2.187952885}
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