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Simplifying 100a2 + -18a + -8 = 0 Reorder the terms: -8 + -18a + 100a2 = 0 Solving -8 + -18a + 100a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -9a + 50a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -9a + 50a2)' equal to zero and attempt to solve: Simplifying -4 + -9a + 50a2 = 0 Solving -4 + -9a + 50a2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.08 + -0.18a + a2 = 0.0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -0.18a + 0.08 + a2 = 0.0 + 0.08 Reorder the terms: -0.08 + 0.08 + -0.18a + a2 = 0.0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -0.18a + a2 = 0.0 + 0.08 -0.18a + a2 = 0.0 + 0.08 Combine like terms: 0.0 + 0.08 = 0.08 -0.18a + a2 = 0.08 The a term is -0.18a. Take half its coefficient (-0.09). Square it (0.0081) and add it to both sides. Add '0.0081' to each side of the equation. -0.18a + 0.0081 + a2 = 0.08 + 0.0081 Reorder the terms: 0.0081 + -0.18a + a2 = 0.08 + 0.0081 Combine like terms: 0.08 + 0.0081 = 0.0881 0.0081 + -0.18a + a2 = 0.0881 Factor a perfect square on the left side: (a + -0.09)(a + -0.09) = 0.0881 Calculate the square root of the right side: 0.296816442 Break this problem into two subproblems by setting (a + -0.09) equal to 0.296816442 and -0.296816442.Subproblem 1
a + -0.09 = 0.296816442 Simplifying a + -0.09 = 0.296816442 Reorder the terms: -0.09 + a = 0.296816442 Solving -0.09 + a = 0.296816442 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.09' to each side of the equation. -0.09 + 0.09 + a = 0.296816442 + 0.09 Combine like terms: -0.09 + 0.09 = 0.00 0.00 + a = 0.296816442 + 0.09 a = 0.296816442 + 0.09 Combine like terms: 0.296816442 + 0.09 = 0.386816442 a = 0.386816442 Simplifying a = 0.386816442Subproblem 2
a + -0.09 = -0.296816442 Simplifying a + -0.09 = -0.296816442 Reorder the terms: -0.09 + a = -0.296816442 Solving -0.09 + a = -0.296816442 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.09' to each side of the equation. -0.09 + 0.09 + a = -0.296816442 + 0.09 Combine like terms: -0.09 + 0.09 = 0.00 0.00 + a = -0.296816442 + 0.09 a = -0.296816442 + 0.09 Combine like terms: -0.296816442 + 0.09 = -0.206816442 a = -0.206816442 Simplifying a = -0.206816442Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.386816442, -0.206816442}Solution
a = {0.386816442, -0.206816442}
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