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Simplifying 4a2 + -20a = -48 Reorder the terms: -20a + 4a2 = -48 Solving -20a + 4a2 = -48 Solving for variable 'a'. Reorder the terms: 48 + -20a + 4a2 = -48 + 48 Combine like terms: -48 + 48 = 0 48 + -20a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(12 + -5a + a2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + -5a + a2)' equal to zero and attempt to solve: Simplifying 12 + -5a + a2 = 0 Solving 12 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -5a + -12 + a2 = 0 + -12 Reorder the terms: 12 + -12 + -5a + a2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -5a + a2 = 0 + -12 -5a + a2 = 0 + -12 Combine like terms: 0 + -12 = -12 -5a + a2 = -12 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = -12 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -12 + 6.25 Combine like terms: -12 + 6.25 = -5.75 6.25 + -5a + a2 = -5.75 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = -5.75 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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