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Simplifying -1a(2 + 11a + 4) + -1(7a + 4) = 0 Reorder the terms: -1a(2 + 4 + 11a) + -1(7a + 4) = 0 Combine like terms: 2 + 4 = 6 -1a(6 + 11a) + -1(7a + 4) = 0 (6 * -1a + 11a * -1a) + -1(7a + 4) = 0 (-6a + -11a2) + -1(7a + 4) = 0 Reorder the terms: -6a + -11a2 + -1(4 + 7a) = 0 -6a + -11a2 + (4 * -1 + 7a * -1) = 0 -6a + -11a2 + (-4 + -7a) = 0 Reorder the terms: -4 + -6a + -7a + -11a2 = 0 Combine like terms: -6a + -7a = -13a -4 + -13a + -11a2 = 0 Solving -4 + -13a + -11a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 13a + 11a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 13a + 11a2)' equal to zero and attempt to solve: Simplifying 4 + 13a + 11a2 = 0 Solving 4 + 13a + 11a2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.3636363636 + 1.181818182a + a2 = 0 Move the constant term to the right: Add '-0.3636363636' to each side of the equation. 0.3636363636 + 1.181818182a + -0.3636363636 + a2 = 0 + -0.3636363636 Reorder the terms: 0.3636363636 + -0.3636363636 + 1.181818182a + a2 = 0 + -0.3636363636 Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000 0.0000000000 + 1.181818182a + a2 = 0 + -0.3636363636 1.181818182a + a2 = 0 + -0.3636363636 Combine like terms: 0 + -0.3636363636 = -0.3636363636 1.181818182a + a2 = -0.3636363636 The a term is 1.181818182a. Take half its coefficient (0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. 1.181818182a + 0.3491735538 + a2 = -0.3636363636 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182a + a2 = -0.3636363636 + 0.3491735538 Combine like terms: -0.3636363636 + 0.3491735538 = -0.0144628098 0.3491735538 + 1.181818182a + a2 = -0.0144628098 Factor a perfect square on the left side: (a + 0.590909091)(a + 0.590909091) = -0.0144628098 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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