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Simplifying a2 + -30a + -180 = 0 Reorder the terms: -180 + -30a + a2 = 0 Solving -180 + -30a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -30a + 180 + a2 = 0 + 180 Reorder the terms: -180 + 180 + -30a + a2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -30a + a2 = 0 + 180 -30a + a2 = 0 + 180 Combine like terms: 0 + 180 = 180 -30a + a2 = 180 The a term is -30a. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30a + 225 + a2 = 180 + 225 Reorder the terms: 225 + -30a + a2 = 180 + 225 Combine like terms: 180 + 225 = 405 225 + -30a + a2 = 405 Factor a perfect square on the left side: (a + -15)(a + -15) = 405 Calculate the square root of the right side: 20.124611797 Break this problem into two subproblems by setting (a + -15) equal to 20.124611797 and -20.124611797.Subproblem 1
a + -15 = 20.124611797 Simplifying a + -15 = 20.124611797 Reorder the terms: -15 + a = 20.124611797 Solving -15 + a = 20.124611797 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + a = 20.124611797 + 15 Combine like terms: -15 + 15 = 0 0 + a = 20.124611797 + 15 a = 20.124611797 + 15 Combine like terms: 20.124611797 + 15 = 35.124611797 a = 35.124611797 Simplifying a = 35.124611797Subproblem 2
a + -15 = -20.124611797 Simplifying a + -15 = -20.124611797 Reorder the terms: -15 + a = -20.124611797 Solving -15 + a = -20.124611797 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + a = -20.124611797 + 15 Combine like terms: -15 + 15 = 0 0 + a = -20.124611797 + 15 a = -20.124611797 + 15 Combine like terms: -20.124611797 + 15 = -5.124611797 a = -5.124611797 Simplifying a = -5.124611797Solution
The solution to the problem is based on the solutions from the subproblems. a = {35.124611797, -5.124611797}
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