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Simplifying 5a2 + 30a + -11 = 0 Reorder the terms: -11 + 30a + 5a2 = 0 Solving -11 + 30a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + 6a + a2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 6a + 2.2 + a2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 6a + a2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 6a + a2 = 0 + 2.2 6a + a2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 6a + a2 = 2.2 The a term is 6a. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6a + 9 + a2 = 2.2 + 9 Reorder the terms: 9 + 6a + a2 = 2.2 + 9 Combine like terms: 2.2 + 9 = 11.2 9 + 6a + a2 = 11.2 Factor a perfect square on the left side: (a + 3)(a + 3) = 11.2 Calculate the square root of the right side: 3.346640106 Break this problem into two subproblems by setting (a + 3) equal to 3.346640106 and -3.346640106.Subproblem 1
a + 3 = 3.346640106 Simplifying a + 3 = 3.346640106 Reorder the terms: 3 + a = 3.346640106 Solving 3 + a = 3.346640106 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 3.346640106 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.346640106 + -3 a = 3.346640106 + -3 Combine like terms: 3.346640106 + -3 = 0.346640106 a = 0.346640106 Simplifying a = 0.346640106Subproblem 2
a + 3 = -3.346640106 Simplifying a + 3 = -3.346640106 Reorder the terms: 3 + a = -3.346640106 Solving 3 + a = -3.346640106 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -3.346640106 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.346640106 + -3 a = -3.346640106 + -3 Combine like terms: -3.346640106 + -3 = -6.346640106 a = -6.346640106 Simplifying a = -6.346640106Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.346640106, -6.346640106}
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