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Simplifying 7a2 + 35 = 7 + -40a Reorder the terms: 35 + 7a2 = 7 + -40a Solving 35 + 7a2 = 7 + -40a Solving for variable 'a'. Reorder the terms: 35 + -7 + 40a + 7a2 = 7 + -40a + -7 + 40a Combine like terms: 35 + -7 = 28 28 + 40a + 7a2 = 7 + -40a + -7 + 40a Reorder the terms: 28 + 40a + 7a2 = 7 + -7 + -40a + 40a Combine like terms: 7 + -7 = 0 28 + 40a + 7a2 = 0 + -40a + 40a 28 + 40a + 7a2 = -40a + 40a Combine like terms: -40a + 40a = 0 28 + 40a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4 + 5.714285714a + a2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 5.714285714a + -4 + a2 = 0 + -4 Reorder the terms: 4 + -4 + 5.714285714a + a2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5.714285714a + a2 = 0 + -4 5.714285714a + a2 = 0 + -4 Combine like terms: 0 + -4 = -4 5.714285714a + a2 = -4 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 = -4 + 8.163265305 Reorder the terms: 8.163265305 + 5.714285714a + a2 = -4 + 8.163265305 Combine like terms: -4 + 8.163265305 = 4.163265305 8.163265305 + 5.714285714a + a2 = 4.163265305 Factor a perfect square on the left side: (a + 2.857142857)(a + 2.857142857) = 4.163265305 Calculate the square root of the right side: 2.040408122 Break this problem into two subproblems by setting (a + 2.857142857) equal to 2.040408122 and -2.040408122.Subproblem 1
a + 2.857142857 = 2.040408122 Simplifying a + 2.857142857 = 2.040408122 Reorder the terms: 2.857142857 + a = 2.040408122 Solving 2.857142857 + a = 2.040408122 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 = 2.040408122 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + a = 2.040408122 + -2.857142857 a = 2.040408122 + -2.857142857 Combine like terms: 2.040408122 + -2.857142857 = -0.816734735 a = -0.816734735 Simplifying a = -0.816734735Subproblem 2
a + 2.857142857 = -2.040408122 Simplifying a + 2.857142857 = -2.040408122 Reorder the terms: 2.857142857 + a = -2.040408122 Solving 2.857142857 + a = -2.040408122 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 = -2.040408122 + -2.857142857 Combine like terms: 2.857142857 + -2.857142857 = 0.000000000 0.000000000 + a = -2.040408122 + -2.857142857 a = -2.040408122 + -2.857142857 Combine like terms: -2.040408122 + -2.857142857 = -4.897550979 a = -4.897550979 Simplifying a = -4.897550979Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.816734735, -4.897550979}
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