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Simplifying 4a2 + -39a + -8 = 0 Reorder the terms: -8 + -39a + 4a2 = 0 Solving -8 + -39a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + -9.75a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -9.75a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -9.75a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -9.75a + a2 = 0 + 2 -9.75a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -9.75a + a2 = 2 The a term is -9.75a. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75a + 23.765625 + a2 = 2 + 23.765625 Reorder the terms: 23.765625 + -9.75a + a2 = 2 + 23.765625 Combine like terms: 2 + 23.765625 = 25.765625 23.765625 + -9.75a + a2 = 25.765625 Factor a perfect square on the left side: (a + -4.875)(a + -4.875) = 25.765625 Calculate the square root of the right side: 5.075985126 Break this problem into two subproblems by setting (a + -4.875) equal to 5.075985126 and -5.075985126.Subproblem 1
a + -4.875 = 5.075985126 Simplifying a + -4.875 = 5.075985126 Reorder the terms: -4.875 + a = 5.075985126 Solving -4.875 + a = 5.075985126 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + a = 5.075985126 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + a = 5.075985126 + 4.875 a = 5.075985126 + 4.875 Combine like terms: 5.075985126 + 4.875 = 9.950985126 a = 9.950985126 Simplifying a = 9.950985126Subproblem 2
a + -4.875 = -5.075985126 Simplifying a + -4.875 = -5.075985126 Reorder the terms: -4.875 + a = -5.075985126 Solving -4.875 + a = -5.075985126 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + a = -5.075985126 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + a = -5.075985126 + 4.875 a = -5.075985126 + 4.875 Combine like terms: -5.075985126 + 4.875 = -0.200985126 a = -0.200985126 Simplifying a = -0.200985126Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.950985126, -0.200985126}
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