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Simplifying 6a10 + a5 + -21 = 0 Reorder the terms: -21 + a5 + 6a10 = 0 Solving -21 + a5 + 6a10 = 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'. -3.5 + 0.1666666667a5 + a10 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 0.1666666667a5 + 3.5 + a10 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 0.1666666667a5 + a10 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 0.1666666667a5 + a10 = 0 + 3.5 0.1666666667a5 + a10 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 0.1666666667a5 + a10 = 3.5 The a term is a5. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667a5 + 0.25 + a10 = 3.5 + 0.25 Reorder the terms: 0.25 + 0.1666666667a5 + a10 = 3.5 + 0.25 Combine like terms: 3.5 + 0.25 = 3.75 0.25 + 0.1666666667a5 + a10 = 3.75 Factor a perfect square on the left side: (a5 + 0.5)(a5 + 0.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (a5 + 0.5) equal to 1.936491673 and -1.936491673.Subproblem 1
a5 + 0.5 = 1.936491673 Simplifying a5 + 0.5 = 1.936491673 Reorder the terms: 0.5 + a5 = 1.936491673 Solving 0.5 + a5 = 1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a5 = 1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a5 = 1.936491673 + -0.5 a5 = 1.936491673 + -0.5 Combine like terms: 1.936491673 + -0.5 = 1.436491673 a5 = 1.436491673 Simplifying a5 = 1.436491673 Reorder the terms: -1.436491673 + a5 = 1.436491673 + -1.436491673 Combine like terms: 1.436491673 + -1.436491673 = 0.000000000 -1.436491673 + a5 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
a5 + 0.5 = -1.936491673 Simplifying a5 + 0.5 = -1.936491673 Reorder the terms: 0.5 + a5 = -1.936491673 Solving 0.5 + a5 = -1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a5 = -1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a5 = -1.936491673 + -0.5 a5 = -1.936491673 + -0.5 Combine like terms: -1.936491673 + -0.5 = -2.436491673 a5 = -2.436491673 Simplifying a5 = -2.436491673 Reorder the terms: 2.436491673 + a5 = -2.436491673 + 2.436491673 Combine like terms: -2.436491673 + 2.436491673 = 0.000000000 2.436491673 + a5 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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