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Simplifying (a2 + -25a) + 56 = 0 Reorder the terms: (-25a + a2) + 56 = 0 Remove parenthesis around (-25a + a2) -25a + a2 + 56 = 0 Reorder the terms: 56 + -25a + a2 = 0 Solving 56 + -25a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -25a + -56 + a2 = 0 + -56 Reorder the terms: 56 + -56 + -25a + a2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -25a + a2 = 0 + -56 -25a + a2 = 0 + -56 Combine like terms: 0 + -56 = -56 -25a + a2 = -56 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 = -56 + 156.25 Reorder the terms: 156.25 + -25a + a2 = -56 + 156.25 Combine like terms: -56 + 156.25 = 100.25 156.25 + -25a + a2 = 100.25 Factor a perfect square on the left side: (a + -12.5)(a + -12.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (a + -12.5) equal to 10.012492197 and -10.012492197.Subproblem 1
a + -12.5 = 10.012492197 Simplifying a + -12.5 = 10.012492197 Reorder the terms: -12.5 + a = 10.012492197 Solving -12.5 + a = 10.012492197 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 = 10.012492197 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = 10.012492197 + 12.5 a = 10.012492197 + 12.5 Combine like terms: 10.012492197 + 12.5 = 22.512492197 a = 22.512492197 Simplifying a = 22.512492197Subproblem 2
a + -12.5 = -10.012492197 Simplifying a + -12.5 = -10.012492197 Reorder the terms: -12.5 + a = -10.012492197 Solving -12.5 + a = -10.012492197 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 = -10.012492197 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + a = -10.012492197 + 12.5 a = -10.012492197 + 12.5 Combine like terms: -10.012492197 + 12.5 = 2.487507803 a = 2.487507803 Simplifying a = 2.487507803Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.512492197, 2.487507803}
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