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Simplifying 7a2 + 5a + -10 = 0 Reorder the terms: -10 + 5a + 7a2 = 0 Solving -10 + 5a + 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'. -1.428571429 + 0.7142857143a + a2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.7142857143a + 1.428571429 + a2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.7142857143a + a2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.7142857143a + a2 = 0 + 1.428571429 0.7142857143a + a2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.7142857143a + a2 = 1.428571429 The a term is 0.7142857143a. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143a + 0.1275510204 + a2 = 1.428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143a + a2 = 1.428571429 + 0.1275510204 Combine like terms: 1.428571429 + 0.1275510204 = 1.5561224494 0.1275510204 + 0.7142857143a + a2 = 1.5561224494 Factor a perfect square on the left side: (a + 0.3571428572)(a + 0.3571428572) = 1.5561224494 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (a + 0.3571428572) equal to 1.247446371 and -1.247446371.Subproblem 1
a + 0.3571428572 = 1.247446371 Simplifying a + 0.3571428572 = 1.247446371 Reorder the terms: 0.3571428572 + a = 1.247446371 Solving 0.3571428572 + a = 1.247446371 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + a = 1.247446371 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + a = 1.247446371 + -0.3571428572 a = 1.247446371 + -0.3571428572 Combine like terms: 1.247446371 + -0.3571428572 = 0.8903035138 a = 0.8903035138 Simplifying a = 0.8903035138Subproblem 2
a + 0.3571428572 = -1.247446371 Simplifying a + 0.3571428572 = -1.247446371 Reorder the terms: 0.3571428572 + a = -1.247446371 Solving 0.3571428572 + a = -1.247446371 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + a = -1.247446371 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + a = -1.247446371 + -0.3571428572 a = -1.247446371 + -0.3571428572 Combine like terms: -1.247446371 + -0.3571428572 = -1.6045892282 a = -1.6045892282 Simplifying a = -1.6045892282Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.8903035138, -1.6045892282}
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