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Simplifying a2 + -30a + 24 = 0 Reorder the terms: 24 + -30a + a2 = 0 Solving 24 + -30a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -30a + -24 + a2 = 0 + -24 Reorder the terms: 24 + -24 + -30a + a2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -30a + a2 = 0 + -24 -30a + a2 = 0 + -24 Combine like terms: 0 + -24 = -24 -30a + a2 = -24 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 = -24 + 225 Reorder the terms: 225 + -30a + a2 = -24 + 225 Combine like terms: -24 + 225 = 201 225 + -30a + a2 = 201 Factor a perfect square on the left side: (a + -15)(a + -15) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (a + -15) equal to 14.177446879 and -14.177446879.Subproblem 1
a + -15 = 14.177446879 Simplifying a + -15 = 14.177446879 Reorder the terms: -15 + a = 14.177446879 Solving -15 + a = 14.177446879 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 = 14.177446879 + 15 Combine like terms: -15 + 15 = 0 0 + a = 14.177446879 + 15 a = 14.177446879 + 15 Combine like terms: 14.177446879 + 15 = 29.177446879 a = 29.177446879 Simplifying a = 29.177446879Subproblem 2
a + -15 = -14.177446879 Simplifying a + -15 = -14.177446879 Reorder the terms: -15 + a = -14.177446879 Solving -15 + a = -14.177446879 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 = -14.177446879 + 15 Combine like terms: -15 + 15 = 0 0 + a = -14.177446879 + 15 a = -14.177446879 + 15 Combine like terms: -14.177446879 + 15 = 0.822553121 a = 0.822553121 Simplifying a = 0.822553121Solution
The solution to the problem is based on the solutions from the subproblems. a = {29.177446879, 0.822553121}
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