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Simplifying 7a2 + 33 = 7 + -40a Reorder the terms: 33 + 7a2 = 7 + -40a Solving 33 + 7a2 = 7 + -40a Solving for variable 'a'. Reorder the terms: 33 + -7 + 40a + 7a2 = 7 + -40a + -7 + 40a Combine like terms: 33 + -7 = 26 26 + 40a + 7a2 = 7 + -40a + -7 + 40a Reorder the terms: 26 + 40a + 7a2 = 7 + -7 + -40a + 40a Combine like terms: 7 + -7 = 0 26 + 40a + 7a2 = 0 + -40a + 40a 26 + 40a + 7a2 = -40a + 40a Combine like terms: -40a + 40a = 0 26 + 40a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.714285714 + 5.714285714a + a2 = 0 Move the constant term to the right: Add '-3.714285714' to each side of the equation. 3.714285714 + 5.714285714a + -3.714285714 + a2 = 0 + -3.714285714 Reorder the terms: 3.714285714 + -3.714285714 + 5.714285714a + a2 = 0 + -3.714285714 Combine like terms: 3.714285714 + -3.714285714 = 0.000000000 0.000000000 + 5.714285714a + a2 = 0 + -3.714285714 5.714285714a + a2 = 0 + -3.714285714 Combine like terms: 0 + -3.714285714 = -3.714285714 5.714285714a + a2 = -3.714285714 The a term is 5.714285714a. Take half its coefficient (2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. 5.714285714a + 8.163265305 + a2 = -3.714285714 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714a + a2 = -3.714285714 + 8.163265305 Combine like terms: -3.714285714 + 8.163265305 = 4.448979591 8.163265305 + 5.714285714a + a2 = 4.448979591 Factor a perfect square on the left side: (a + 2.857142857)(a + 2.857142857) = 4.448979591 Calculate the square root of the right side: 2.109260437 Break this problem into two subproblems by setting (a + 2.857142857) equal to 2.109260437 and -2.109260437.Subproblem 1
a + 2.857142857 = 2.109260437 Simplifying a + 2.857142857 = 2.109260437 Reorder the terms: 2.857142857 + a = 2.109260437 Solving 2.857142857 + a = 2.109260437 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + a = 2.109260437 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + a = 2.109260437 + -2.857142857 a = 2.109260437 + -2.857142857 Combine like terms: 2.109260437 + -2.857142857 = -0.74788242 a = -0.74788242 Simplifying a = -0.74788242Subproblem 2
a + 2.857142857 = -2.109260437 Simplifying a + 2.857142857 = -2.109260437 Reorder the terms: 2.857142857 + a = -2.109260437 Solving 2.857142857 + a = -2.109260437 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.857142857' to each side of the equation. 2.857142857 + -2.857142857 + a = -2.109260437 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + a = -2.109260437 + -2.857142857 a = -2.109260437 + -2.857142857 Combine like terms: -2.109260437 + -2.857142857 = -4.966403294 a = -4.966403294 Simplifying a = -4.966403294Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.74788242, -4.966403294}
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