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Simplifying 11a2 + -1a + -7 = 0 Reorder the terms: -7 + -1a + 11a2 = 0 Solving -7 + -1a + 11a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.6363636364 + -0.09090909091a + a2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + -0.09090909091a + 0.6363636364 + a2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + -0.09090909091a + a2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + -0.09090909091a + a2 = 0 + 0.6363636364 -0.09090909091a + a2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 -0.09090909091a + a2 = 0.6363636364 The a term is -0.09090909091a. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091a + 0.002066115703 + a2 = 0.6363636364 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091a + a2 = 0.6363636364 + 0.002066115703 Combine like terms: 0.6363636364 + 0.002066115703 = 0.638429752103 0.002066115703 + -0.09090909091a + a2 = 0.638429752103 Factor a perfect square on the left side: (a + -0.04545454546)(a + -0.04545454546) = 0.638429752103 Calculate the square root of the right side: 0.799017992 Break this problem into two subproblems by setting (a + -0.04545454546) equal to 0.799017992 and -0.799017992.Subproblem 1
a + -0.04545454546 = 0.799017992 Simplifying a + -0.04545454546 = 0.799017992 Reorder the terms: -0.04545454546 + a = 0.799017992 Solving -0.04545454546 + a = 0.799017992 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + a = 0.799017992 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + a = 0.799017992 + 0.04545454546 a = 0.799017992 + 0.04545454546 Combine like terms: 0.799017992 + 0.04545454546 = 0.84447253746 a = 0.84447253746 Simplifying a = 0.84447253746Subproblem 2
a + -0.04545454546 = -0.799017992 Simplifying a + -0.04545454546 = -0.799017992 Reorder the terms: -0.04545454546 + a = -0.799017992 Solving -0.04545454546 + a = -0.799017992 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + a = -0.799017992 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + a = -0.799017992 + 0.04545454546 a = -0.799017992 + 0.04545454546 Combine like terms: -0.799017992 + 0.04545454546 = -0.75356344654 a = -0.75356344654 Simplifying a = -0.75356344654Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.84447253746, -0.75356344654}
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