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Simplifying 2a2 + -7a + -14a + 14 = 0 Reorder the terms: 14 + -7a + -14a + 2a2 = 0 Combine like terms: -7a + -14a = -21a 14 + -21a + 2a2 = 0 Solving 14 + -21a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + -10.5a + a2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -10.5a + -7 + a2 = 0 + -7 Reorder the terms: 7 + -7 + -10.5a + a2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -10.5a + a2 = 0 + -7 -10.5a + a2 = 0 + -7 Combine like terms: 0 + -7 = -7 -10.5a + a2 = -7 The a term is -10.5a. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5a + 27.5625 + a2 = -7 + 27.5625 Reorder the terms: 27.5625 + -10.5a + a2 = -7 + 27.5625 Combine like terms: -7 + 27.5625 = 20.5625 27.5625 + -10.5a + a2 = 20.5625 Factor a perfect square on the left side: (a + -5.25)(a + -5.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (a + -5.25) equal to 4.534589287 and -4.534589287.Subproblem 1
a + -5.25 = 4.534589287 Simplifying a + -5.25 = 4.534589287 Reorder the terms: -5.25 + a = 4.534589287 Solving -5.25 + a = 4.534589287 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + a = 4.534589287 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + a = 4.534589287 + 5.25 a = 4.534589287 + 5.25 Combine like terms: 4.534589287 + 5.25 = 9.784589287 a = 9.784589287 Simplifying a = 9.784589287Subproblem 2
a + -5.25 = -4.534589287 Simplifying a + -5.25 = -4.534589287 Reorder the terms: -5.25 + a = -4.534589287 Solving -5.25 + a = -4.534589287 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + a = -4.534589287 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + a = -4.534589287 + 5.25 a = -4.534589287 + 5.25 Combine like terms: -4.534589287 + 5.25 = 0.715410713 a = 0.715410713 Simplifying a = 0.715410713Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.784589287, 0.715410713}
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