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Simplifying 0 = 148 + -51a + 4a2 Solving 0 = 148 + -51a + 4a2 Solving for variable 'a'. Combine like terms: 0 + -148 = -148 -148 + 51a + -4a2 = 148 + -51a + 4a2 + -148 + 51a + -4a2 Reorder the terms: -148 + 51a + -4a2 = 148 + -148 + -51a + 51a + 4a2 + -4a2 Combine like terms: 148 + -148 = 0 -148 + 51a + -4a2 = 0 + -51a + 51a + 4a2 + -4a2 -148 + 51a + -4a2 = -51a + 51a + 4a2 + -4a2 Combine like terms: -51a + 51a = 0 -148 + 51a + -4a2 = 0 + 4a2 + -4a2 -148 + 51a + -4a2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 -148 + 51a + -4a2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 37 + -12.75a + a2 = 0 Move the constant term to the right: Add '-37' to each side of the equation. 37 + -12.75a + -37 + a2 = 0 + -37 Reorder the terms: 37 + -37 + -12.75a + a2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -12.75a + a2 = 0 + -37 -12.75a + a2 = 0 + -37 Combine like terms: 0 + -37 = -37 -12.75a + a2 = -37 The a term is -12.75a. Take half its coefficient (-6.375). Square it (40.640625) and add it to both sides. Add '40.640625' to each side of the equation. -12.75a + 40.640625 + a2 = -37 + 40.640625 Reorder the terms: 40.640625 + -12.75a + a2 = -37 + 40.640625 Combine like terms: -37 + 40.640625 = 3.640625 40.640625 + -12.75a + a2 = 3.640625 Factor a perfect square on the left side: (a + -6.375)(a + -6.375) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (a + -6.375) equal to 1.90804219 and -1.90804219.Subproblem 1
a + -6.375 = 1.90804219 Simplifying a + -6.375 = 1.90804219 Reorder the terms: -6.375 + a = 1.90804219 Solving -6.375 + a = 1.90804219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + a = 1.90804219 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + a = 1.90804219 + 6.375 a = 1.90804219 + 6.375 Combine like terms: 1.90804219 + 6.375 = 8.28304219 a = 8.28304219 Simplifying a = 8.28304219Subproblem 2
a + -6.375 = -1.90804219 Simplifying a + -6.375 = -1.90804219 Reorder the terms: -6.375 + a = -1.90804219 Solving -6.375 + a = -1.90804219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6.375' to each side of the equation. -6.375 + 6.375 + a = -1.90804219 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + a = -1.90804219 + 6.375 a = -1.90804219 + 6.375 Combine like terms: -1.90804219 + 6.375 = 4.46695781 a = 4.46695781 Simplifying a = 4.46695781Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.28304219, 4.46695781}
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