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Simplifying a2 + -35a + 280 = 0 Reorder the terms: 280 + -35a + a2 = 0 Solving 280 + -35a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-280' to each side of the equation. 280 + -35a + -280 + a2 = 0 + -280 Reorder the terms: 280 + -280 + -35a + a2 = 0 + -280 Combine like terms: 280 + -280 = 0 0 + -35a + a2 = 0 + -280 -35a + a2 = 0 + -280 Combine like terms: 0 + -280 = -280 -35a + a2 = -280 The a term is -35a. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35a + 306.25 + a2 = -280 + 306.25 Reorder the terms: 306.25 + -35a + a2 = -280 + 306.25 Combine like terms: -280 + 306.25 = 26.25 306.25 + -35a + a2 = 26.25 Factor a perfect square on the left side: (a + -17.5)(a + -17.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (a + -17.5) equal to 5.123475383 and -5.123475383.Subproblem 1
a + -17.5 = 5.123475383 Simplifying a + -17.5 = 5.123475383 Reorder the terms: -17.5 + a = 5.123475383 Solving -17.5 + a = 5.123475383 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + a = 5.123475383 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + a = 5.123475383 + 17.5 a = 5.123475383 + 17.5 Combine like terms: 5.123475383 + 17.5 = 22.623475383 a = 22.623475383 Simplifying a = 22.623475383Subproblem 2
a + -17.5 = -5.123475383 Simplifying a + -17.5 = -5.123475383 Reorder the terms: -17.5 + a = -5.123475383 Solving -17.5 + a = -5.123475383 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + a = -5.123475383 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + a = -5.123475383 + 17.5 a = -5.123475383 + 17.5 Combine like terms: -5.123475383 + 17.5 = 12.376524617 a = 12.376524617 Simplifying a = 12.376524617Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.623475383, 12.376524617}
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