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Simplifying a2 + -15a + -50 = 0 Reorder the terms: -50 + -15a + a2 = 0 Solving -50 + -15a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -15a + 50 + a2 = 0 + 50 Reorder the terms: -50 + 50 + -15a + a2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -15a + a2 = 0 + 50 -15a + a2 = 0 + 50 Combine like terms: 0 + 50 = 50 -15a + a2 = 50 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 = 50 + 56.25 Reorder the terms: 56.25 + -15a + a2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + -15a + a2 = 106.25 Factor a perfect square on the left side: (a + -7.5)(a + -7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (a + -7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
a + -7.5 = 10.307764064 Simplifying a + -7.5 = 10.307764064 Reorder the terms: -7.5 + a = 10.307764064 Solving -7.5 + a = 10.307764064 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 = 10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = 10.307764064 + 7.5 a = 10.307764064 + 7.5 Combine like terms: 10.307764064 + 7.5 = 17.807764064 a = 17.807764064 Simplifying a = 17.807764064Subproblem 2
a + -7.5 = -10.307764064 Simplifying a + -7.5 = -10.307764064 Reorder the terms: -7.5 + a = -10.307764064 Solving -7.5 + a = -10.307764064 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 = -10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + a = -10.307764064 + 7.5 a = -10.307764064 + 7.5 Combine like terms: -10.307764064 + 7.5 = -2.807764064 a = -2.807764064 Simplifying a = -2.807764064Solution
The solution to the problem is based on the solutions from the subproblems. a = {17.807764064, -2.807764064}
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