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Simplifying 7a2 + -13 = -10a Reorder the terms: -13 + 7a2 = -10a Solving -13 + 7a2 = -10a Solving for variable 'a'. Reorder the terms: -13 + 10a + 7a2 = -10a + 10a Combine like terms: -10a + 10a = 0 -13 + 10a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + 1.428571429a + a2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + 1.428571429a + 1.857142857 + a2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + 1.428571429a + a2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + 1.428571429a + a2 = 0 + 1.857142857 1.428571429a + a2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 1.428571429a + a2 = 1.857142857 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 = 1.857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429a + a2 = 1.857142857 + 0.5102040819 Combine like terms: 1.857142857 + 0.5102040819 = 2.3673469389 0.5102040819 + 1.428571429a + a2 = 2.3673469389 Factor a perfect square on the left side: (a + 0.7142857145)(a + 0.7142857145) = 2.3673469389 Calculate the square root of the right side: 1.538618516 Break this problem into two subproblems by setting (a + 0.7142857145) equal to 1.538618516 and -1.538618516.Subproblem 1
a + 0.7142857145 = 1.538618516 Simplifying a + 0.7142857145 = 1.538618516 Reorder the terms: 0.7142857145 + a = 1.538618516 Solving 0.7142857145 + a = 1.538618516 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 = 1.538618516 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + a = 1.538618516 + -0.7142857145 a = 1.538618516 + -0.7142857145 Combine like terms: 1.538618516 + -0.7142857145 = 0.8243328015 a = 0.8243328015 Simplifying a = 0.8243328015Subproblem 2
a + 0.7142857145 = -1.538618516 Simplifying a + 0.7142857145 = -1.538618516 Reorder the terms: 0.7142857145 + a = -1.538618516 Solving 0.7142857145 + a = -1.538618516 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 = -1.538618516 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + a = -1.538618516 + -0.7142857145 a = -1.538618516 + -0.7142857145 Combine like terms: -1.538618516 + -0.7142857145 = -2.2529042305 a = -2.2529042305 Simplifying a = -2.2529042305Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.8243328015, -2.2529042305}
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