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Simplifying 6a2 + 51a + 10 = 0 Reorder the terms: 10 + 51a + 6a2 = 0 Solving 10 + 51a + 6a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.666666667 + 8.5a + a2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 8.5a + -1.666666667 + a2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 8.5a + a2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 8.5a + a2 = 0 + -1.666666667 8.5a + a2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 8.5a + a2 = -1.666666667 The a term is 8.5a. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5a + 18.0625 + a2 = -1.666666667 + 18.0625 Reorder the terms: 18.0625 + 8.5a + a2 = -1.666666667 + 18.0625 Combine like terms: -1.666666667 + 18.0625 = 16.395833333 18.0625 + 8.5a + a2 = 16.395833333 Factor a perfect square on the left side: (a + 4.25)(a + 4.25) = 16.395833333 Calculate the square root of the right side: 4.049176871 Break this problem into two subproblems by setting (a + 4.25) equal to 4.049176871 and -4.049176871.Subproblem 1
a + 4.25 = 4.049176871 Simplifying a + 4.25 = 4.049176871 Reorder the terms: 4.25 + a = 4.049176871 Solving 4.25 + a = 4.049176871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + a = 4.049176871 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + a = 4.049176871 + -4.25 a = 4.049176871 + -4.25 Combine like terms: 4.049176871 + -4.25 = -0.200823129 a = -0.200823129 Simplifying a = -0.200823129Subproblem 2
a + 4.25 = -4.049176871 Simplifying a + 4.25 = -4.049176871 Reorder the terms: 4.25 + a = -4.049176871 Solving 4.25 + a = -4.049176871 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + a = -4.049176871 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + a = -4.049176871 + -4.25 a = -4.049176871 + -4.25 Combine like terms: -4.049176871 + -4.25 = -8.299176871 a = -8.299176871 Simplifying a = -8.299176871Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.200823129, -8.299176871}
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