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Simplifying a(4 + -1a) + -5(a + 7) = 0 (4 * a + -1a * a) + -5(a + 7) = 0 (4a + -1a2) + -5(a + 7) = 0 Reorder the terms: 4a + -1a2 + -5(7 + a) = 0 4a + -1a2 + (7 * -5 + a * -5) = 0 4a + -1a2 + (-35 + -5a) = 0 Reorder the terms: -35 + 4a + -5a + -1a2 = 0 Combine like terms: 4a + -5a = -1a -35 + -1a + -1a2 = 0 Solving -35 + -1a + -1a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(35 + a + a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(35 + a + a2)' equal to zero and attempt to solve: Simplifying 35 + a + a2 = 0 Solving 35 + a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + a + -35 + a2 = 0 + -35 Reorder the terms: 35 + -35 + a + a2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + a + a2 = 0 + -35 a + a2 = 0 + -35 Combine like terms: 0 + -35 = -35 a + a2 = -35 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. a + 0.25 + a2 = -35 + 0.25 Reorder the terms: 0.25 + a + a2 = -35 + 0.25 Combine like terms: -35 + 0.25 = -34.75 0.25 + a + a2 = -34.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = -34.75 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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