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Simplifying -7a2 + -8a + -6 = 0 Reorder the terms: -6 + -8a + -7a2 = 0 Solving -6 + -8a + -7a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 8a + 7a2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 8a + 7a2)' equal to zero and attempt to solve: Simplifying 6 + 8a + 7a2 = 0 Solving 6 + 8a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 1.142857143a + a2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 1.142857143a + -0.8571428571 + a2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 1.142857143a + a2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 1.142857143a + a2 = 0 + -0.8571428571 1.142857143a + a2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 1.142857143a + a2 = -0.8571428571 The a term is 1.142857143a. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143a + 0.3265306123 + a2 = -0.8571428571 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143a + a2 = -0.8571428571 + 0.3265306123 Combine like terms: -0.8571428571 + 0.3265306123 = -0.5306122448 0.3265306123 + 1.142857143a + a2 = -0.5306122448 Factor a perfect square on the left side: (a + 0.5714285715)(a + 0.5714285715) = -0.5306122448 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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