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Simplifying a2 + -15a + -30 = 0 Reorder the terms: -30 + -15a + a2 = 0 Solving -30 + -15a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -15a + 30 + a2 = 0 + 30 Reorder the terms: -30 + 30 + -15a + a2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -15a + a2 = 0 + 30 -15a + a2 = 0 + 30 Combine like terms: 0 + 30 = 30 -15a + a2 = 30 The a term is -15a. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15a + 56.25 + a2 = 30 + 56.25 Reorder the terms: 56.25 + -15a + a2 = 30 + 56.25 Combine like terms: 30 + 56.25 = 86.25 56.25 + -15a + a2 = 86.25 Factor a perfect square on the left side: (a + -7.5)(a + -7.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (a + -7.5) equal to 9.287087811 and -9.287087811.Subproblem 1
a + -7.5 = 9.287087811 Simplifying a + -7.5 = 9.287087811 Reorder the terms: -7.5 + a = 9.287087811 Solving -7.5 + a = 9.287087811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + a = 9.287087811 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = 9.287087811 + 7.5 a = 9.287087811 + 7.5 Combine like terms: 9.287087811 + 7.5 = 16.787087811 a = 16.787087811 Simplifying a = 16.787087811Subproblem 2
a + -7.5 = -9.287087811 Simplifying a + -7.5 = -9.287087811 Reorder the terms: -7.5 + a = -9.287087811 Solving -7.5 + a = -9.287087811 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + a = -9.287087811 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = -9.287087811 + 7.5 a = -9.287087811 + 7.5 Combine like terms: -9.287087811 + 7.5 = -1.787087811 a = -1.787087811 Simplifying a = -1.787087811Solution
The solution to the problem is based on the solutions from the subproblems. a = {16.787087811, -1.787087811}
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