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Simplifying (8a3 + 5)(8a3 + -0.5) = 0 Reorder the terms: (5 + 8a3)(8a3 + -0.5) = 0 Reorder the terms: (5 + 8a3)(-0.5 + 8a3) = 0 Multiply (5 + 8a3) * (-0.5 + 8a3) (5(-0.5 + 8a3) + 8a3 * (-0.5 + 8a3)) = 0 ((-0.5 * 5 + 8a3 * 5) + 8a3 * (-0.5 + 8a3)) = 0 ((-2.5 + 40a3) + 8a3 * (-0.5 + 8a3)) = 0 (-2.5 + 40a3 + (-0.5 * 8a3 + 8a3 * 8a3)) = 0 (-2.5 + 40a3 + (-4a3 + 64a6)) = 0 Combine like terms: 40a3 + -4a3 = 36a3 (-2.5 + 36a3 + 64a6) = 0 Solving -2.5 + 36a3 + 64a6 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.0390625 + 0.5625a3 + a6 = 0 Move the constant term to the right: Add '0.0390625' to each side of the equation. -0.0390625 + 0.5625a3 + 0.0390625 + a6 = 0 + 0.0390625 Reorder the terms: -0.0390625 + 0.0390625 + 0.5625a3 + a6 = 0 + 0.0390625 Combine like terms: -0.0390625 + 0.0390625 = 0.0000000 0.0000000 + 0.5625a3 + a6 = 0 + 0.0390625 0.5625a3 + a6 = 0 + 0.0390625 Combine like terms: 0 + 0.0390625 = 0.0390625 0.5625a3 + a6 = 0.0390625 The a term is 0.5625a3. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625a3 + 0.0791015625 + a6 = 0.0390625 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625a3 + a6 = 0.0390625 + 0.0791015625 Combine like terms: 0.0390625 + 0.0791015625 = 0.1181640625 0.0791015625 + 0.5625a3 + a6 = 0.1181640625 Factor a perfect square on the left side: (a3 + 0.28125)(a3 + 0.28125) = 0.1181640625 Calculate the square root of the right side: 0.34375 Break this problem into two subproblems by setting (a3 + 0.28125) equal to 0.34375 and -0.34375.Subproblem 1
a3 + 0.28125 = 0.34375 Simplifying a3 + 0.28125 = 0.34375 Reorder the terms: 0.28125 + a3 = 0.34375 Solving 0.28125 + a3 = 0.34375 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + a3 = 0.34375 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + a3 = 0.34375 + -0.28125 a3 = 0.34375 + -0.28125 Combine like terms: 0.34375 + -0.28125 = 0.0625 a3 = 0.0625 Simplifying a3 = 0.0625 Reorder the terms: -0.0625 + a3 = 0.0625 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 -0.0625 + a3 = 0.0000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
a3 + 0.28125 = -0.34375 Simplifying a3 + 0.28125 = -0.34375 Reorder the terms: 0.28125 + a3 = -0.34375 Solving 0.28125 + a3 = -0.34375 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + a3 = -0.34375 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + a3 = -0.34375 + -0.28125 a3 = -0.34375 + -0.28125 Combine like terms: -0.34375 + -0.28125 = -0.625 a3 = -0.625 Simplifying a3 = -0.625 Reorder the terms: 0.625 + a3 = -0.625 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.625 + a3 = 0.000 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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