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Simplifying 42a2 + -22a + 10 = 0 Reorder the terms: 10 + -22a + 42a2 = 0 Solving 10 + -22a + 42a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -11a + 21a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -11a + 21a2)' equal to zero and attempt to solve: Simplifying 5 + -11a + 21a2 = 0 Solving 5 + -11a + 21a2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.2380952381 + -0.5238095238a + a2 = 0 Move the constant term to the right: Add '-0.2380952381' to each side of the equation. 0.2380952381 + -0.5238095238a + -0.2380952381 + a2 = 0 + -0.2380952381 Reorder the terms: 0.2380952381 + -0.2380952381 + -0.5238095238a + a2 = 0 + -0.2380952381 Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000 0.0000000000 + -0.5238095238a + a2 = 0 + -0.2380952381 -0.5238095238a + a2 = 0 + -0.2380952381 Combine like terms: 0 + -0.2380952381 = -0.2380952381 -0.5238095238a + a2 = -0.2380952381 The a term is -0.5238095238a. Take half its coefficient (-0.2619047619). Square it (0.06859410431) and add it to both sides. Add '0.06859410431' to each side of the equation. -0.5238095238a + 0.06859410431 + a2 = -0.2380952381 + 0.06859410431 Reorder the terms: 0.06859410431 + -0.5238095238a + a2 = -0.2380952381 + 0.06859410431 Combine like terms: -0.2380952381 + 0.06859410431 = -0.16950113379 0.06859410431 + -0.5238095238a + a2 = -0.16950113379 Factor a perfect square on the left side: (a + -0.2619047619)(a + -0.2619047619) = -0.16950113379 Can't calculate square root of the right side. 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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