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Simplifying 4a2 + -16a = 10 Reorder the terms: -16a + 4a2 = 10 Solving -16a + 4a2 = 10 Solving for variable 'a'. Reorder the terms: -10 + -16a + 4a2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -16a + 4a2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -8a + 2a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -8a + 2a2)' equal to zero and attempt to solve: Simplifying -5 + -8a + 2a2 = 0 Solving -5 + -8a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -4a + a2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -4a + 2.5 + a2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -4a + a2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -4a + a2 = 0 + 2.5 -4a + a2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -4a + a2 = 2.5 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 2.5 + 4 Reorder the terms: 4 + -4a + a2 = 2.5 + 4 Combine like terms: 2.5 + 4 = 6.5 4 + -4a + a2 = 6.5 Factor a perfect square on the left side: (a + -2)(a + -2) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (a + -2) equal to 2.549509757 and -2.549509757.Subproblem 1
a + -2 = 2.549509757 Simplifying a + -2 = 2.549509757 Reorder the terms: -2 + a = 2.549509757 Solving -2 + a = 2.549509757 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.549509757 + 2 a = 2.549509757 + 2 Combine like terms: 2.549509757 + 2 = 4.549509757 a = 4.549509757 Simplifying a = 4.549509757Subproblem 2
a + -2 = -2.549509757 Simplifying a + -2 = -2.549509757 Reorder the terms: -2 + a = -2.549509757 Solving -2 + a = -2.549509757 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -2.549509757 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.549509757 + 2 a = -2.549509757 + 2 Combine like terms: -2.549509757 + 2 = -0.549509757 a = -0.549509757 Simplifying a = -0.549509757Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.549509757, -0.549509757}Solution
a = {4.549509757, -0.549509757}
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