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Simplifying 27a2 + 350a + -195 = 0 Reorder the terms: -195 + 350a + 27a2 = 0 Solving -195 + 350a + 27a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -7.222222222 + 12.96296296a + a2 = 0 Move the constant term to the right: Add '7.222222222' to each side of the equation. -7.222222222 + 12.96296296a + 7.222222222 + a2 = 0 + 7.222222222 Reorder the terms: -7.222222222 + 7.222222222 + 12.96296296a + a2 = 0 + 7.222222222 Combine like terms: -7.222222222 + 7.222222222 = 0.000000000 0.000000000 + 12.96296296a + a2 = 0 + 7.222222222 12.96296296a + a2 = 0 + 7.222222222 Combine like terms: 0 + 7.222222222 = 7.222222222 12.96296296a + a2 = 7.222222222 The a term is 12.96296296a. Take half its coefficient (6.48148148). Square it (42.00960218) and add it to both sides. Add '42.00960218' to each side of the equation. 12.96296296a + 42.00960218 + a2 = 7.222222222 + 42.00960218 Reorder the terms: 42.00960218 + 12.96296296a + a2 = 7.222222222 + 42.00960218 Combine like terms: 7.222222222 + 42.00960218 = 49.231824402 42.00960218 + 12.96296296a + a2 = 49.231824402 Factor a perfect square on the left side: (a + 6.48148148)(a + 6.48148148) = 49.231824402 Calculate the square root of the right side: 7.016539347 Break this problem into two subproblems by setting (a + 6.48148148) equal to 7.016539347 and -7.016539347.Subproblem 1
a + 6.48148148 = 7.016539347 Simplifying a + 6.48148148 = 7.016539347 Reorder the terms: 6.48148148 + a = 7.016539347 Solving 6.48148148 + a = 7.016539347 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.48148148' to each side of the equation. 6.48148148 + -6.48148148 + a = 7.016539347 + -6.48148148 Combine like terms: 6.48148148 + -6.48148148 = 0.00000000 0.00000000 + a = 7.016539347 + -6.48148148 a = 7.016539347 + -6.48148148 Combine like terms: 7.016539347 + -6.48148148 = 0.535057867 a = 0.535057867 Simplifying a = 0.535057867Subproblem 2
a + 6.48148148 = -7.016539347 Simplifying a + 6.48148148 = -7.016539347 Reorder the terms: 6.48148148 + a = -7.016539347 Solving 6.48148148 + a = -7.016539347 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.48148148' to each side of the equation. 6.48148148 + -6.48148148 + a = -7.016539347 + -6.48148148 Combine like terms: 6.48148148 + -6.48148148 = 0.00000000 0.00000000 + a = -7.016539347 + -6.48148148 a = -7.016539347 + -6.48148148 Combine like terms: -7.016539347 + -6.48148148 = -13.498020827 a = -13.498020827 Simplifying a = -13.498020827Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.535057867, -13.498020827}
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