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Simplifying 7a2 + -18a + 7 = 0 Reorder the terms: 7 + -18a + 7a2 = 0 Solving 7 + -18a + 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 + -2.571428571a + a2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.571428571a + -1 + a2 = 0 + -1 Reorder the terms: 1 + -1 + -2.571428571a + a2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.571428571a + a2 = 0 + -1 -2.571428571a + a2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.571428571a + a2 = -1 The a term is -2.571428571a. Take half its coefficient (-1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. -2.571428571a + 1.653061225 + a2 = -1 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571a + a2 = -1 + 1.653061225 Combine like terms: -1 + 1.653061225 = 0.653061225 1.653061225 + -2.571428571a + a2 = 0.653061225 Factor a perfect square on the left side: (a + -1.285714286)(a + -1.285714286) = 0.653061225 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (a + -1.285714286) equal to 0.808122036 and -0.808122036.Subproblem 1
a + -1.285714286 = 0.808122036 Simplifying a + -1.285714286 = 0.808122036 Reorder the terms: -1.285714286 + a = 0.808122036 Solving -1.285714286 + a = 0.808122036 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + a = 0.808122036 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + a = 0.808122036 + 1.285714286 a = 0.808122036 + 1.285714286 Combine like terms: 0.808122036 + 1.285714286 = 2.093836322 a = 2.093836322 Simplifying a = 2.093836322Subproblem 2
a + -1.285714286 = -0.808122036 Simplifying a + -1.285714286 = -0.808122036 Reorder the terms: -1.285714286 + a = -0.808122036 Solving -1.285714286 + a = -0.808122036 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + a = -0.808122036 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + a = -0.808122036 + 1.285714286 a = -0.808122036 + 1.285714286 Combine like terms: -0.808122036 + 1.285714286 = 0.47759225 a = 0.47759225 Simplifying a = 0.47759225Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.093836322, 0.47759225}
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