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Simplifying 25a2 + -20a + 415 = 0 Reorder the terms: 415 + -20a + 25a2 = 0 Solving 415 + -20a + 25a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5'. 5(83 + -4a + 5a2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(83 + -4a + 5a2)' equal to zero and attempt to solve: Simplifying 83 + -4a + 5a2 = 0 Solving 83 + -4a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 16.6 + -0.8a + a2 = 0 Move the constant term to the right: Add '-16.6' to each side of the equation. 16.6 + -0.8a + -16.6 + a2 = 0 + -16.6 Reorder the terms: 16.6 + -16.6 + -0.8a + a2 = 0 + -16.6 Combine like terms: 16.6 + -16.6 = 0.0 0.0 + -0.8a + a2 = 0 + -16.6 -0.8a + a2 = 0 + -16.6 Combine like terms: 0 + -16.6 = -16.6 -0.8a + a2 = -16.6 The a term is -0.8a. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8a + 0.16 + a2 = -16.6 + 0.16 Reorder the terms: 0.16 + -0.8a + a2 = -16.6 + 0.16 Combine like terms: -16.6 + 0.16 = -16.44 0.16 + -0.8a + a2 = -16.44 Factor a perfect square on the left side: (a + -0.4)(a + -0.4) = -16.44 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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