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Simplifying a2 + 30a + -72 = 0 Reorder the terms: -72 + 30a + a2 = 0 Solving -72 + 30a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 30a + 72 + a2 = 0 + 72 Reorder the terms: -72 + 72 + 30a + a2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 30a + a2 = 0 + 72 30a + a2 = 0 + 72 Combine like terms: 0 + 72 = 72 30a + a2 = 72 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 = 72 + 225 Reorder the terms: 225 + 30a + a2 = 72 + 225 Combine like terms: 72 + 225 = 297 225 + 30a + a2 = 297 Factor a perfect square on the left side: (a + 15)(a + 15) = 297 Calculate the square root of the right side: 17.23368794 Break this problem into two subproblems by setting (a + 15) equal to 17.23368794 and -17.23368794.Subproblem 1
a + 15 = 17.23368794 Simplifying a + 15 = 17.23368794 Reorder the terms: 15 + a = 17.23368794 Solving 15 + a = 17.23368794 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 = 17.23368794 + -15 Combine like terms: 15 + -15 = 0 0 + a = 17.23368794 + -15 a = 17.23368794 + -15 Combine like terms: 17.23368794 + -15 = 2.23368794 a = 2.23368794 Simplifying a = 2.23368794Subproblem 2
a + 15 = -17.23368794 Simplifying a + 15 = -17.23368794 Reorder the terms: 15 + a = -17.23368794 Solving 15 + a = -17.23368794 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 = -17.23368794 + -15 Combine like terms: 15 + -15 = 0 0 + a = -17.23368794 + -15 a = -17.23368794 + -15 Combine like terms: -17.23368794 + -15 = -32.23368794 a = -32.23368794 Simplifying a = -32.23368794Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.23368794, -32.23368794}
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