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Simplifying -2a(a + -3) = 14 Reorder the terms: -2a(-3 + a) = 14 (-3 * -2a + a * -2a) = 14 (6a + -2a2) = 14 Solving 6a + -2a2 = 14 Solving for variable 'a'. Reorder the terms: -14 + 6a + -2a2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 6a + -2a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 3a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 3a + -1a2)' equal to zero and attempt to solve: Simplifying -7 + 3a + -1a2 = 0 Solving -7 + 3a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -3a + a2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -3a + -7 + a2 = 0 + -7 Reorder the terms: 7 + -7 + -3a + a2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3a + a2 = 0 + -7 -3a + a2 = 0 + -7 Combine like terms: 0 + -7 = -7 -3a + a2 = -7 The a term is -3a. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3a + 2.25 + a2 = -7 + 2.25 Reorder the terms: 2.25 + -3a + a2 = -7 + 2.25 Combine like terms: -7 + 2.25 = -4.75 2.25 + -3a + a2 = -4.75 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = -4.75 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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