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Simplifying 2a2 + 7a + -7 = 0 Reorder the terms: -7 + 7a + 2a2 = 0 Solving -7 + 7a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 3.5a + a2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3.5a + 3.5 + a2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3.5a + a2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3.5a + a2 = 0 + 3.5 3.5a + a2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3.5a + a2 = 3.5 The a term is 3.5a. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5a + 3.0625 + a2 = 3.5 + 3.0625 Reorder the terms: 3.0625 + 3.5a + a2 = 3.5 + 3.0625 Combine like terms: 3.5 + 3.0625 = 6.5625 3.0625 + 3.5a + a2 = 6.5625 Factor a perfect square on the left side: (a + 1.75)(a + 1.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (a + 1.75) equal to 2.561737691 and -2.561737691.Subproblem 1
a + 1.75 = 2.561737691 Simplifying a + 1.75 = 2.561737691 Reorder the terms: 1.75 + a = 2.561737691 Solving 1.75 + a = 2.561737691 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + a = 2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + a = 2.561737691 + -1.75 a = 2.561737691 + -1.75 Combine like terms: 2.561737691 + -1.75 = 0.811737691 a = 0.811737691 Simplifying a = 0.811737691Subproblem 2
a + 1.75 = -2.561737691 Simplifying a + 1.75 = -2.561737691 Reorder the terms: 1.75 + a = -2.561737691 Solving 1.75 + a = -2.561737691 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + a = -2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + a = -2.561737691 + -1.75 a = -2.561737691 + -1.75 Combine like terms: -2.561737691 + -1.75 = -4.311737691 a = -4.311737691 Simplifying a = -4.311737691Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.811737691, -4.311737691}
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