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Simplifying -6a(-5 + 9a) = 34 (-5 * -6a + 9a * -6a) = 34 (30a + -54a2) = 34 Solving 30a + -54a2 = 34 Solving for variable 'a'. Reorder the terms: -34 + 30a + -54a2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 30a + -54a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 15a + -27a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 15a + -27a2)' equal to zero and attempt to solve: Simplifying -17 + 15a + -27a2 = 0 Solving -17 + 15a + -27a2 = 0 Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. 0.6296296296 + -0.5555555556a + a2 = 0 Move the constant term to the right: Add '-0.6296296296' to each side of the equation. 0.6296296296 + -0.5555555556a + -0.6296296296 + a2 = 0 + -0.6296296296 Reorder the terms: 0.6296296296 + -0.6296296296 + -0.5555555556a + a2 = 0 + -0.6296296296 Combine like terms: 0.6296296296 + -0.6296296296 = 0.0000000000 0.0000000000 + -0.5555555556a + a2 = 0 + -0.6296296296 -0.5555555556a + a2 = 0 + -0.6296296296 Combine like terms: 0 + -0.6296296296 = -0.6296296296 -0.5555555556a + a2 = -0.6296296296 The a term is -0.5555555556a. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556a + 0.07716049384 + a2 = -0.6296296296 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556a + a2 = -0.6296296296 + 0.07716049384 Combine like terms: -0.6296296296 + 0.07716049384 = -0.55246913576 0.07716049384 + -0.5555555556a + a2 = -0.55246913576 Factor a perfect square on the left side: (a + -0.2777777778)(a + -0.2777777778) = -0.55246913576 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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