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Simplifying 7(a2) + -15a + 5 = 0 Reorder the terms: 5 + -15a + 7a2 = 0 Solving 5 + -15a + 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'. 0.7142857143 + -2.142857143a + a2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -2.142857143a + -0.7142857143 + a2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -2.142857143a + a2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -2.142857143a + a2 = 0 + -0.7142857143 -2.142857143a + a2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -2.142857143a + a2 = -0.7142857143 The a term is -2.142857143a. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143a + 1.147959185 + a2 = -0.7142857143 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143a + a2 = -0.7142857143 + 1.147959185 Combine like terms: -0.7142857143 + 1.147959185 = 0.4336734707 1.147959185 + -2.142857143a + a2 = 0.4336734707 Factor a perfect square on the left side: (a + -1.071428572)(a + -1.071428572) = 0.4336734707 Calculate the square root of the right side: 0.658538891 Break this problem into two subproblems by setting (a + -1.071428572) equal to 0.658538891 and -0.658538891.Subproblem 1
a + -1.071428572 = 0.658538891 Simplifying a + -1.071428572 = 0.658538891 Reorder the terms: -1.071428572 + a = 0.658538891 Solving -1.071428572 + a = 0.658538891 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + a = 0.658538891 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + a = 0.658538891 + 1.071428572 a = 0.658538891 + 1.071428572 Combine like terms: 0.658538891 + 1.071428572 = 1.729967463 a = 1.729967463 Simplifying a = 1.729967463Subproblem 2
a + -1.071428572 = -0.658538891 Simplifying a + -1.071428572 = -0.658538891 Reorder the terms: -1.071428572 + a = -0.658538891 Solving -1.071428572 + a = -0.658538891 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + a = -0.658538891 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + a = -0.658538891 + 1.071428572 a = -0.658538891 + 1.071428572 Combine like terms: -0.658538891 + 1.071428572 = 0.412889681 a = 0.412889681 Simplifying a = 0.412889681Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.729967463, 0.412889681}
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