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Simplifying 96 + 8a + -42a2 = 0 Solving 96 + 8a + -42a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(48 + 4a + -21a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + 4a + -21a2)' equal to zero and attempt to solve: Simplifying 48 + 4a + -21a2 = 0 Solving 48 + 4a + -21a2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -2.285714286 + -0.1904761905a + a2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -0.1904761905a + 2.285714286 + a2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -0.1904761905a + a2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -0.1904761905a + a2 = 0 + 2.285714286 -0.1904761905a + a2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -0.1904761905a + a2 = 2.285714286 The a term is -0.1904761905a. Take half its coefficient (-0.09523809525). Square it (0.009070294787) and add it to both sides. Add '0.009070294787' to each side of the equation. -0.1904761905a + 0.009070294787 + a2 = 2.285714286 + 0.009070294787 Reorder the terms: 0.009070294787 + -0.1904761905a + a2 = 2.285714286 + 0.009070294787 Combine like terms: 2.285714286 + 0.009070294787 = 2.294784580787 0.009070294787 + -0.1904761905a + a2 = 2.294784580787 Factor a perfect square on the left side: (a + -0.09523809525)(a + -0.09523809525) = 2.294784580787 Calculate the square root of the right side: 1.51485464 Break this problem into two subproblems by setting (a + -0.09523809525) equal to 1.51485464 and -1.51485464.Subproblem 1
a + -0.09523809525 = 1.51485464 Simplifying a + -0.09523809525 = 1.51485464 Reorder the terms: -0.09523809525 + a = 1.51485464 Solving -0.09523809525 + a = 1.51485464 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.09523809525' to each side of the equation. -0.09523809525 + 0.09523809525 + a = 1.51485464 + 0.09523809525 Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000 0.00000000000 + a = 1.51485464 + 0.09523809525 a = 1.51485464 + 0.09523809525 Combine like terms: 1.51485464 + 0.09523809525 = 1.61009273525 a = 1.61009273525 Simplifying a = 1.61009273525Subproblem 2
a + -0.09523809525 = -1.51485464 Simplifying a + -0.09523809525 = -1.51485464 Reorder the terms: -0.09523809525 + a = -1.51485464 Solving -0.09523809525 + a = -1.51485464 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.09523809525' to each side of the equation. -0.09523809525 + 0.09523809525 + a = -1.51485464 + 0.09523809525 Combine like terms: -0.09523809525 + 0.09523809525 = 0.00000000000 0.00000000000 + a = -1.51485464 + 0.09523809525 a = -1.51485464 + 0.09523809525 Combine like terms: -1.51485464 + 0.09523809525 = -1.41961654475 a = -1.41961654475 Simplifying a = -1.41961654475Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.61009273525, -1.41961654475}Solution
a = {1.61009273525, -1.41961654475}
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