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Simplifying 2a(a + -5) + 4(9 + -5) = 0 Reorder the terms: 2a(-5 + a) + 4(9 + -5) = 0 (-5 * 2a + a * 2a) + 4(9 + -5) = 0 (-10a + 2a2) + 4(9 + -5) = 0 Combine like terms: 9 + -5 = 4 -10a + 2a2 + 4(4) = 0 Multiply 4 * 4 -10a + 2a2 + 16 = 0 Reorder the terms: 16 + -10a + 2a2 = 0 Solving 16 + -10a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -5a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -5a + a2)' equal to zero and attempt to solve: Simplifying 8 + -5a + a2 = 0 Solving 8 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -5a + -8 + a2 = 0 + -8 Reorder the terms: 8 + -8 + -5a + a2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5a + a2 = 0 + -8 -5a + a2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5a + a2 = -8 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 = -8 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + -5a + a2 = -1.75 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = -1.75 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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