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Simplifying 2a2 + 2a + -35 = 0 Reorder the terms: -35 + 2a + 2a2 = 0 Solving -35 + 2a + 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'. -17.5 + a + a2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + a + 17.5 + a2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + a + a2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + a + a2 = 0 + 17.5 a + a2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 a + a2 = 17.5 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 17.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 17.5 + 0.25 Combine like terms: 17.5 + 0.25 = 17.75 1.25 + a2 = 17.75 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (a + 0.5) equal to 4.213074887 and -4.213074887.Subproblem 1
a + 0.5 = 4.213074887 Simplifying a + 0.5 = 4.213074887 Reorder the terms: 0.5 + a = 4.213074887 Solving 0.5 + a = 4.213074887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 4.213074887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 4.213074887 + -0.5 a = 4.213074887 + -0.5 Combine like terms: 4.213074887 + -0.5 = 3.713074887 a = 3.713074887 Simplifying a = 3.713074887Subproblem 2
a + 0.5 = -4.213074887 Simplifying a + 0.5 = -4.213074887 Reorder the terms: 0.5 + a = -4.213074887 Solving 0.5 + a = -4.213074887 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -4.213074887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -4.213074887 + -0.5 a = -4.213074887 + -0.5 Combine like terms: -4.213074887 + -0.5 = -4.713074887 a = -4.713074887 Simplifying a = -4.713074887Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.713074887, -4.713074887}
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