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Simplifying 4a2 + 18a + 90 = 0 Reorder the terms: 90 + 18a + 4a2 = 0 Solving 90 + 18a + 4a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + 9a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + 9a + 2a2)' equal to zero and attempt to solve: Simplifying 45 + 9a + 2a2 = 0 Solving 45 + 9a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 4.5a + a2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 4.5a + -22.5 + a2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 4.5a + a2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 4.5a + a2 = 0 + -22.5 4.5a + a2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 4.5a + a2 = -22.5 The a term is 4.5a. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5a + 5.0625 + a2 = -22.5 + 5.0625 Reorder the terms: 5.0625 + 4.5a + a2 = -22.5 + 5.0625 Combine like terms: -22.5 + 5.0625 = -17.4375 5.0625 + 4.5a + a2 = -17.4375 Factor a perfect square on the left side: (a + 2.25)(a + 2.25) = -17.4375 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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