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Simplifying 2a2 + 20a + 100 = 40 Reorder the terms: 100 + 20a + 2a2 = 40 Solving 100 + 20a + 2a2 = 40 Solving for variable 'a'. Reorder the terms: 100 + -40 + 20a + 2a2 = 40 + -40 Combine like terms: 100 + -40 = 60 60 + 20a + 2a2 = 40 + -40 Combine like terms: 40 + -40 = 0 60 + 20a + 2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(30 + 10a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + 10a + a2)' equal to zero and attempt to solve: Simplifying 30 + 10a + a2 = 0 Solving 30 + 10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 10a + -30 + a2 = 0 + -30 Reorder the terms: 30 + -30 + 10a + a2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 10a + a2 = 0 + -30 10a + a2 = 0 + -30 Combine like terms: 0 + -30 = -30 10a + a2 = -30 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = -30 + 25 Reorder the terms: 25 + 10a + a2 = -30 + 25 Combine like terms: -30 + 25 = -5 25 + 10a + a2 = -5 Factor a perfect square on the left side: (a + 5)(a + 5) = -5 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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