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Simplifying 160 = 55a + -5a2 Solving 160 = 55a + -5a2 Solving for variable 'a'. Reorder the terms: 160 + -55a + 5a2 = 55a + -55a + -5a2 + 5a2 Combine like terms: 55a + -55a = 0 160 + -55a + 5a2 = 0 + -5a2 + 5a2 160 + -55a + 5a2 = -5a2 + 5a2 Combine like terms: -5a2 + 5a2 = 0 160 + -55a + 5a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(32 + -11a + a2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(32 + -11a + a2)' equal to zero and attempt to solve: Simplifying 32 + -11a + a2 = 0 Solving 32 + -11a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -11a + -32 + a2 = 0 + -32 Reorder the terms: 32 + -32 + -11a + a2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -11a + a2 = 0 + -32 -11a + a2 = 0 + -32 Combine like terms: 0 + -32 = -32 -11a + a2 = -32 The a term is -11a. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11a + 30.25 + a2 = -32 + 30.25 Reorder the terms: 30.25 + -11a + a2 = -32 + 30.25 Combine like terms: -32 + 30.25 = -1.75 30.25 + -11a + a2 = -1.75 Factor a perfect square on the left side: (a + -5.5)(a + -5.5) = -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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