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Simplifying 2a2 + -30a + 180 = 0 Reorder the terms: 180 + -30a + 2a2 = 0 Solving 180 + -30a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -15a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -15a + a2)' equal to zero and attempt to solve: Simplifying 90 + -15a + a2 = 0 Solving 90 + -15a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + -15a + -90 + a2 = 0 + -90 Reorder the terms: 90 + -90 + -15a + a2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -15a + a2 = 0 + -90 -15a + a2 = 0 + -90 Combine like terms: 0 + -90 = -90 -15a + a2 = -90 The a term is -15a. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15a + 56.25 + a2 = -90 + 56.25 Reorder the terms: 56.25 + -15a + a2 = -90 + 56.25 Combine like terms: -90 + 56.25 = -33.75 56.25 + -15a + a2 = -33.75 Factor a perfect square on the left side: (a + -7.5)(a + -7.5) = -33.75 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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