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Simplifying -4a2 + -8a + 2 = 9 Reorder the terms: 2 + -8a + -4a2 = 9 Solving 2 + -8a + -4a2 = 9 Solving for variable 'a'. Reorder the terms: 2 + -9 + -8a + -4a2 = 9 + -9 Combine like terms: 2 + -9 = -7 -7 + -8a + -4a2 = 9 + -9 Combine like terms: 9 + -9 = 0 -7 + -8a + -4a2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 8a + 4a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 8a + 4a2)' equal to zero and attempt to solve: Simplifying 7 + 8a + 4a2 = 0 Solving 7 + 8a + 4a2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 2a + a2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 2a + -1.75 + a2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 2a + a2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 2a + a2 = 0 + -1.75 2a + a2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 2a + a2 = -1.75 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = -1.75 + 1 Reorder the terms: 1 + 2a + a2 = -1.75 + 1 Combine like terms: -1.75 + 1 = -0.75 1 + 2a + a2 = -0.75 Factor a perfect square on the left side: (a + 1)(a + 1) = -0.75 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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