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Simplifying 7a2 + 13a = 10 Reorder the terms: 13a + 7a2 = 10 Solving 13a + 7a2 = 10 Solving for variable 'a'. Reorder the terms: -10 + 13a + 7a2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 13a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 1.857142857a + a2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 1.857142857a + 1.428571429 + a2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 1.857142857a + a2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 1.857142857a + a2 = 0 + 1.428571429 1.857142857a + a2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 1.857142857a + a2 = 1.428571429 The a term is 1.857142857a. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857a + 0.8622448978 + a2 = 1.428571429 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857a + a2 = 1.428571429 + 0.8622448978 Combine like terms: 1.428571429 + 0.8622448978 = 2.2908163268 0.8622448978 + 1.857142857a + a2 = 2.2908163268 Factor a perfect square on the left side: (a + 0.9285714285)(a + 0.9285714285) = 2.2908163268 Calculate the square root of the right side: 1.513544293 Break this problem into two subproblems by setting (a + 0.9285714285) equal to 1.513544293 and -1.513544293.Subproblem 1
a + 0.9285714285 = 1.513544293 Simplifying a + 0.9285714285 = 1.513544293 Reorder the terms: 0.9285714285 + a = 1.513544293 Solving 0.9285714285 + a = 1.513544293 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + a = 1.513544293 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + a = 1.513544293 + -0.9285714285 a = 1.513544293 + -0.9285714285 Combine like terms: 1.513544293 + -0.9285714285 = 0.5849728645 a = 0.5849728645 Simplifying a = 0.5849728645Subproblem 2
a + 0.9285714285 = -1.513544293 Simplifying a + 0.9285714285 = -1.513544293 Reorder the terms: 0.9285714285 + a = -1.513544293 Solving 0.9285714285 + a = -1.513544293 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + a = -1.513544293 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + a = -1.513544293 + -0.9285714285 a = -1.513544293 + -0.9285714285 Combine like terms: -1.513544293 + -0.9285714285 = -2.4421157215 a = -2.4421157215 Simplifying a = -2.4421157215Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.5849728645, -2.4421157215}
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