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Simplifying 7a2 + 50a = 7 Reorder the terms: 50a + 7a2 = 7 Solving 50a + 7a2 = 7 Solving for variable 'a'. Reorder the terms: -7 + 50a + 7a2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 50a + 7a2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 7.142857143a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 7.142857143a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 7.142857143a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7.142857143a + a2 = 0 + 1 7.142857143a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 7.142857143a + a2 = 1 The a term is 7.142857143a. Take half its coefficient (3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. 7.142857143a + 12.75510204 + a2 = 1 + 12.75510204 Reorder the terms: 12.75510204 + 7.142857143a + a2 = 1 + 12.75510204 Combine like terms: 1 + 12.75510204 = 13.75510204 12.75510204 + 7.142857143a + a2 = 13.75510204 Factor a perfect square on the left side: (a + 3.571428572)(a + 3.571428572) = 13.75510204 Calculate the square root of the right side: 3.708787139 Break this problem into two subproblems by setting (a + 3.571428572) equal to 3.708787139 and -3.708787139.Subproblem 1
a + 3.571428572 = 3.708787139 Simplifying a + 3.571428572 = 3.708787139 Reorder the terms: 3.571428572 + a = 3.708787139 Solving 3.571428572 + a = 3.708787139 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + a = 3.708787139 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + a = 3.708787139 + -3.571428572 a = 3.708787139 + -3.571428572 Combine like terms: 3.708787139 + -3.571428572 = 0.137358567 a = 0.137358567 Simplifying a = 0.137358567Subproblem 2
a + 3.571428572 = -3.708787139 Simplifying a + 3.571428572 = -3.708787139 Reorder the terms: 3.571428572 + a = -3.708787139 Solving 3.571428572 + a = -3.708787139 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + a = -3.708787139 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + a = -3.708787139 + -3.571428572 a = -3.708787139 + -3.571428572 Combine like terms: -3.708787139 + -3.571428572 = -7.280215711 a = -7.280215711 Simplifying a = -7.280215711Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.137358567, -7.280215711}
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