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Simplifying 7a2 = 2a + 30 Reorder the terms: 7a2 = 30 + 2a Solving 7a2 = 30 + 2a Solving for variable 'a'. Reorder the terms: -30 + -2a + 7a2 = 30 + 2a + -30 + -2a Reorder the terms: -30 + -2a + 7a2 = 30 + -30 + 2a + -2a Combine like terms: 30 + -30 = 0 -30 + -2a + 7a2 = 0 + 2a + -2a -30 + -2a + 7a2 = 2a + -2a Combine like terms: 2a + -2a = 0 -30 + -2a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.285714286 + -0.2857142857a + a2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -0.2857142857a + 4.285714286 + a2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -0.2857142857a + a2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -0.2857142857a + a2 = 0 + 4.285714286 -0.2857142857a + a2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -0.2857142857a + a2 = 4.285714286 The a term is -0.2857142857a. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857a + 0.02040816328 + a2 = 4.285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857a + a2 = 4.285714286 + 0.02040816328 Combine like terms: 4.285714286 + 0.02040816328 = 4.30612244928 0.02040816328 + -0.2857142857a + a2 = 4.30612244928 Factor a perfect square on the left side: (a + -0.1428571429)(a + -0.1428571429) = 4.30612244928 Calculate the square root of the right side: 2.075119864 Break this problem into two subproblems by setting (a + -0.1428571429) equal to 2.075119864 and -2.075119864.Subproblem 1
a + -0.1428571429 = 2.075119864 Simplifying a + -0.1428571429 = 2.075119864 Reorder the terms: -0.1428571429 + a = 2.075119864 Solving -0.1428571429 + a = 2.075119864 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + a = 2.075119864 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + a = 2.075119864 + 0.1428571429 a = 2.075119864 + 0.1428571429 Combine like terms: 2.075119864 + 0.1428571429 = 2.2179770069 a = 2.2179770069 Simplifying a = 2.2179770069Subproblem 2
a + -0.1428571429 = -2.075119864 Simplifying a + -0.1428571429 = -2.075119864 Reorder the terms: -0.1428571429 + a = -2.075119864 Solving -0.1428571429 + a = -2.075119864 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + a = -2.075119864 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + a = -2.075119864 + 0.1428571429 a = -2.075119864 + 0.1428571429 Combine like terms: -2.075119864 + 0.1428571429 = -1.9322627211 a = -1.9322627211 Simplifying a = -1.9322627211Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.2179770069, -1.9322627211}
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