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Simplifying 7a2 + 10a + 2 = 0 Reorder the terms: 2 + 10a + 7a2 = 0 Solving 2 + 10a + 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'. 0.2857142857 + 1.428571429a + a2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.428571429a + -0.2857142857 + a2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.428571429a + a2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.428571429a + a2 = 0 + -0.2857142857 1.428571429a + a2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.428571429a + a2 = -0.2857142857 The a term is 1.428571429a. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429a + 0.5102040819 + a2 = -0.2857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429a + a2 = -0.2857142857 + 0.5102040819 Combine like terms: -0.2857142857 + 0.5102040819 = 0.2244897962 0.5102040819 + 1.428571429a + a2 = 0.2244897962 Factor a perfect square on the left side: (a + 0.7142857145)(a + 0.7142857145) = 0.2244897962 Calculate the square root of the right side: 0.473803542 Break this problem into two subproblems by setting (a + 0.7142857145) equal to 0.473803542 and -0.473803542.Subproblem 1
a + 0.7142857145 = 0.473803542 Simplifying a + 0.7142857145 = 0.473803542 Reorder the terms: 0.7142857145 + a = 0.473803542 Solving 0.7142857145 + a = 0.473803542 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + a = 0.473803542 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + a = 0.473803542 + -0.7142857145 a = 0.473803542 + -0.7142857145 Combine like terms: 0.473803542 + -0.7142857145 = -0.2404821725 a = -0.2404821725 Simplifying a = -0.2404821725Subproblem 2
a + 0.7142857145 = -0.473803542 Simplifying a + 0.7142857145 = -0.473803542 Reorder the terms: 0.7142857145 + a = -0.473803542 Solving 0.7142857145 + a = -0.473803542 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + a = -0.473803542 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + a = -0.473803542 + -0.7142857145 a = -0.473803542 + -0.7142857145 Combine like terms: -0.473803542 + -0.7142857145 = -1.1880892565 a = -1.1880892565 Simplifying a = -1.1880892565Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.2404821725, -1.1880892565}
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