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Simplifying 7a2 + 2a + -11 = 0 Reorder the terms: -11 + 2a + 7a2 = 0 Solving -11 + 2a + 7a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.571428571 + 0.2857142857a + a2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + 0.2857142857a + 1.571428571 + a2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + 0.2857142857a + a2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + 0.2857142857a + a2 = 0 + 1.571428571 0.2857142857a + a2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 0.2857142857a + a2 = 1.571428571 The a term is 0.2857142857a. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857a + 0.02040816328 + a2 = 1.571428571 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857a + a2 = 1.571428571 + 0.02040816328 Combine like terms: 1.571428571 + 0.02040816328 = 1.59183673428 0.02040816328 + 0.2857142857a + a2 = 1.59183673428 Factor a perfect square on the left side: (a + 0.1428571429)(a + 0.1428571429) = 1.59183673428 Calculate the square root of the right side: 1.261680124 Break this problem into two subproblems by setting (a + 0.1428571429) equal to 1.261680124 and -1.261680124.Subproblem 1
a + 0.1428571429 = 1.261680124 Simplifying a + 0.1428571429 = 1.261680124 Reorder the terms: 0.1428571429 + a = 1.261680124 Solving 0.1428571429 + a = 1.261680124 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + a = 1.261680124 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + a = 1.261680124 + -0.1428571429 a = 1.261680124 + -0.1428571429 Combine like terms: 1.261680124 + -0.1428571429 = 1.1188229811 a = 1.1188229811 Simplifying a = 1.1188229811Subproblem 2
a + 0.1428571429 = -1.261680124 Simplifying a + 0.1428571429 = -1.261680124 Reorder the terms: 0.1428571429 + a = -1.261680124 Solving 0.1428571429 + a = -1.261680124 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + a = -1.261680124 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + a = -1.261680124 + -0.1428571429 a = -1.261680124 + -0.1428571429 Combine like terms: -1.261680124 + -0.1428571429 = -1.4045372669 a = -1.4045372669 Simplifying a = -1.4045372669Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.1188229811, -1.4045372669}
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