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Simplifying 3a2 + -42a + 222 = 0 Reorder the terms: 222 + -42a + 3a2 = 0 Solving 222 + -42a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(74 + -14a + a2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(74 + -14a + a2)' equal to zero and attempt to solve: Simplifying 74 + -14a + a2 = 0 Solving 74 + -14a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-74' to each side of the equation. 74 + -14a + -74 + a2 = 0 + -74 Reorder the terms: 74 + -74 + -14a + a2 = 0 + -74 Combine like terms: 74 + -74 = 0 0 + -14a + a2 = 0 + -74 -14a + a2 = 0 + -74 Combine like terms: 0 + -74 = -74 -14a + a2 = -74 The a term is -14a. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14a + 49 + a2 = -74 + 49 Reorder the terms: 49 + -14a + a2 = -74 + 49 Combine like terms: -74 + 49 = -25 49 + -14a + a2 = -25 Factor a perfect square on the left side: (a + -7)(a + -7) = -25 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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