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Simplifying 20a2 + 20a = -62 Reorder the terms: 20a + 20a2 = -62 Solving 20a + 20a2 = -62 Solving for variable 'a'. Reorder the terms: 62 + 20a + 20a2 = -62 + 62 Combine like terms: -62 + 62 = 0 62 + 20a + 20a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(31 + 10a + 10a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + 10a + 10a2)' equal to zero and attempt to solve: Simplifying 31 + 10a + 10a2 = 0 Solving 31 + 10a + 10a2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 3.1 + a + a2 = 0.0 Move the constant term to the right: Add '-3.1' to each side of the equation. 3.1 + a + -3.1 + a2 = 0.0 + -3.1 Reorder the terms: 3.1 + -3.1 + a + a2 = 0.0 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + a + a2 = 0.0 + -3.1 a + a2 = 0.0 + -3.1 Combine like terms: 0.0 + -3.1 = -3.1 a + a2 = -3.1 The a term is a. 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. + 0.25 + a2 = -3.1 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = -3.1 + 0.25 Combine like terms: -3.1 + 0.25 = -2.85 1.25 + a2 = -2.85 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -2.85 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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