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Simplifying 6a2 + -21 = 7a Reorder the terms: -21 + 6a2 = 7a Solving -21 + 6a2 = 7a Solving for variable 'a'. Reorder the terms: -21 + -7a + 6a2 = 7a + -7a Combine like terms: 7a + -7a = 0 -21 + -7a + 6a2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.5 + -1.166666667a + a2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -1.166666667a + 3.5 + a2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -1.166666667a + a2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -1.166666667a + a2 = 0 + 3.5 -1.166666667a + a2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -1.166666667a + a2 = 3.5 The a term is -1.166666667a. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667a + 0.3402777780 + a2 = 3.5 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667a + a2 = 3.5 + 0.3402777780 Combine like terms: 3.5 + 0.3402777780 = 3.840277778 0.3402777780 + -1.166666667a + a2 = 3.840277778 Factor a perfect square on the left side: (a + -0.5833333335)(a + -0.5833333335) = 3.840277778 Calculate the square root of the right side: 1.959662669 Break this problem into two subproblems by setting (a + -0.5833333335) equal to 1.959662669 and -1.959662669.Subproblem 1
a + -0.5833333335 = 1.959662669 Simplifying a + -0.5833333335 = 1.959662669 Reorder the terms: -0.5833333335 + a = 1.959662669 Solving -0.5833333335 + a = 1.959662669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + a = 1.959662669 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = 1.959662669 + 0.5833333335 a = 1.959662669 + 0.5833333335 Combine like terms: 1.959662669 + 0.5833333335 = 2.5429960025 a = 2.5429960025 Simplifying a = 2.5429960025Subproblem 2
a + -0.5833333335 = -1.959662669 Simplifying a + -0.5833333335 = -1.959662669 Reorder the terms: -0.5833333335 + a = -1.959662669 Solving -0.5833333335 + a = -1.959662669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + a = -1.959662669 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = -1.959662669 + 0.5833333335 a = -1.959662669 + 0.5833333335 Combine like terms: -1.959662669 + 0.5833333335 = -1.3763293355 a = -1.3763293355 Simplifying a = -1.3763293355Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.5429960025, -1.3763293355}
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