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Simplifying 8a2 + -11a + -9 = -3 Reorder the terms: -9 + -11a + 8a2 = -3 Solving -9 + -11a + 8a2 = -3 Solving for variable 'a'. Reorder the terms: -9 + 3 + -11a + 8a2 = -3 + 3 Combine like terms: -9 + 3 = -6 -6 + -11a + 8a2 = -3 + 3 Combine like terms: -3 + 3 = 0 -6 + -11a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -1.375a + a2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.375a + 0.75 + a2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.375a + a2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.375a + a2 = 0 + 0.75 -1.375a + a2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.375a + a2 = 0.75 The a term is -1.375a. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375a + 0.47265625 + a2 = 0.75 + 0.47265625 Reorder the terms: 0.47265625 + -1.375a + a2 = 0.75 + 0.47265625 Combine like terms: 0.75 + 0.47265625 = 1.22265625 0.47265625 + -1.375a + a2 = 1.22265625 Factor a perfect square on the left side: (a + -0.6875)(a + -0.6875) = 1.22265625 Calculate the square root of the right side: 1.105737876 Break this problem into two subproblems by setting (a + -0.6875) equal to 1.105737876 and -1.105737876.Subproblem 1
a + -0.6875 = 1.105737876 Simplifying a + -0.6875 = 1.105737876 Reorder the terms: -0.6875 + a = 1.105737876 Solving -0.6875 + a = 1.105737876 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + a = 1.105737876 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + a = 1.105737876 + 0.6875 a = 1.105737876 + 0.6875 Combine like terms: 1.105737876 + 0.6875 = 1.793237876 a = 1.793237876 Simplifying a = 1.793237876Subproblem 2
a + -0.6875 = -1.105737876 Simplifying a + -0.6875 = -1.105737876 Reorder the terms: -0.6875 + a = -1.105737876 Solving -0.6875 + a = -1.105737876 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + a = -1.105737876 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + a = -1.105737876 + 0.6875 a = -1.105737876 + 0.6875 Combine like terms: -1.105737876 + 0.6875 = -0.418237876 a = -0.418237876 Simplifying a = -0.418237876Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.793237876, -0.418237876}
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