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Simplifying a2 + -25a + 35 = 0 Reorder the terms: 35 + -25a + a2 = 0 Solving 35 + -25a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -25a + -35 + a2 = 0 + -35 Reorder the terms: 35 + -35 + -25a + a2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -25a + a2 = 0 + -35 -25a + a2 = 0 + -35 Combine like terms: 0 + -35 = -35 -25a + a2 = -35 The a term is -25a. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25a + 156.25 + a2 = -35 + 156.25 Reorder the terms: 156.25 + -25a + a2 = -35 + 156.25 Combine like terms: -35 + 156.25 = 121.25 156.25 + -25a + a2 = 121.25 Factor a perfect square on the left side: (a + -12.5)(a + -12.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (a + -12.5) equal to 11.011357773 and -11.011357773.Subproblem 1
a + -12.5 = 11.011357773 Simplifying a + -12.5 = 11.011357773 Reorder the terms: -12.5 + a = 11.011357773 Solving -12.5 + a = 11.011357773 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + a = 11.011357773 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = 11.011357773 + 12.5 a = 11.011357773 + 12.5 Combine like terms: 11.011357773 + 12.5 = 23.511357773 a = 23.511357773 Simplifying a = 23.511357773Subproblem 2
a + -12.5 = -11.011357773 Simplifying a + -12.5 = -11.011357773 Reorder the terms: -12.5 + a = -11.011357773 Solving -12.5 + a = -11.011357773 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + a = -11.011357773 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = -11.011357773 + 12.5 a = -11.011357773 + 12.5 Combine like terms: -11.011357773 + 12.5 = 1.488642227 a = 1.488642227 Simplifying a = 1.488642227Solution
The solution to the problem is based on the solutions from the subproblems. a = {23.511357773, 1.488642227}
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