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Simplifying 2a2 + -36a + -10 = 0 Reorder the terms: -10 + -36a + 2a2 = 0 Solving -10 + -36a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -18a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -18a + a2)' equal to zero and attempt to solve: Simplifying -5 + -18a + a2 = 0 Solving -5 + -18a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -18a + 5 + a2 = 0 + 5 Reorder the terms: -5 + 5 + -18a + a2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -18a + a2 = 0 + 5 -18a + a2 = 0 + 5 Combine like terms: 0 + 5 = 5 -18a + a2 = 5 The a term is -18a. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18a + 81 + a2 = 5 + 81 Reorder the terms: 81 + -18a + a2 = 5 + 81 Combine like terms: 5 + 81 = 86 81 + -18a + a2 = 86 Factor a perfect square on the left side: (a + -9)(a + -9) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (a + -9) equal to 9.273618495 and -9.273618495.Subproblem 1
a + -9 = 9.273618495 Simplifying a + -9 = 9.273618495 Reorder the terms: -9 + a = 9.273618495 Solving -9 + a = 9.273618495 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = 9.273618495 + 9 Combine like terms: -9 + 9 = 0 0 + a = 9.273618495 + 9 a = 9.273618495 + 9 Combine like terms: 9.273618495 + 9 = 18.273618495 a = 18.273618495 Simplifying a = 18.273618495Subproblem 2
a + -9 = -9.273618495 Simplifying a + -9 = -9.273618495 Reorder the terms: -9 + a = -9.273618495 Solving -9 + a = -9.273618495 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + a = -9.273618495 + 9 Combine like terms: -9 + 9 = 0 0 + a = -9.273618495 + 9 a = -9.273618495 + 9 Combine like terms: -9.273618495 + 9 = -0.273618495 a = -0.273618495 Simplifying a = -0.273618495Solution
The solution to the problem is based on the solutions from the subproblems. a = {18.273618495, -0.273618495}Solution
a = {18.273618495, -0.273618495}
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