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Simplifying -8a2 + -26a + 280 = 0 Reorder the terms: 280 + -26a + -8a2 = 0 Solving 280 + -26a + -8a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(140 + -13a + -4a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(140 + -13a + -4a2)' equal to zero and attempt to solve: Simplifying 140 + -13a + -4a2 = 0 Solving 140 + -13a + -4a2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -35 + 3.25a + a2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 3.25a + 35 + a2 = 0 + 35 Reorder the terms: -35 + 35 + 3.25a + a2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 3.25a + a2 = 0 + 35 3.25a + a2 = 0 + 35 Combine like terms: 0 + 35 = 35 3.25a + a2 = 35 The a term is 3.25a. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25a + 2.640625 + a2 = 35 + 2.640625 Reorder the terms: 2.640625 + 3.25a + a2 = 35 + 2.640625 Combine like terms: 35 + 2.640625 = 37.640625 2.640625 + 3.25a + a2 = 37.640625 Factor a perfect square on the left side: (a + 1.625)(a + 1.625) = 37.640625 Calculate the square root of the right side: 6.135195596 Break this problem into two subproblems by setting (a + 1.625) equal to 6.135195596 and -6.135195596.Subproblem 1
a + 1.625 = 6.135195596 Simplifying a + 1.625 = 6.135195596 Reorder the terms: 1.625 + a = 6.135195596 Solving 1.625 + a = 6.135195596 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + a = 6.135195596 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + a = 6.135195596 + -1.625 a = 6.135195596 + -1.625 Combine like terms: 6.135195596 + -1.625 = 4.510195596 a = 4.510195596 Simplifying a = 4.510195596Subproblem 2
a + 1.625 = -6.135195596 Simplifying a + 1.625 = -6.135195596 Reorder the terms: 1.625 + a = -6.135195596 Solving 1.625 + a = -6.135195596 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + a = -6.135195596 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + a = -6.135195596 + -1.625 a = -6.135195596 + -1.625 Combine like terms: -6.135195596 + -1.625 = -7.760195596 a = -7.760195596 Simplifying a = -7.760195596Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.510195596, -7.760195596}Solution
a = {4.510195596, -7.760195596}
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