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Simplifying a2 + 5a + -25 = 0 Reorder the terms: -25 + 5a + a2 = 0 Solving -25 + 5a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 5a + 25 + a2 = 0 + 25 Reorder the terms: -25 + 25 + 5a + a2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 5a + a2 = 0 + 25 5a + a2 = 0 + 25 Combine like terms: 0 + 25 = 25 5a + a2 = 25 The a term is 5a. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5a + 6.25 + a2 = 25 + 6.25 Reorder the terms: 6.25 + 5a + a2 = 25 + 6.25 Combine like terms: 25 + 6.25 = 31.25 6.25 + 5a + a2 = 31.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (a + 2.5) equal to 5.590169944 and -5.590169944.Subproblem 1
a + 2.5 = 5.590169944 Simplifying a + 2.5 = 5.590169944 Reorder the terms: 2.5 + a = 5.590169944 Solving 2.5 + a = 5.590169944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 5.590169944 + -2.5 a = 5.590169944 + -2.5 Combine like terms: 5.590169944 + -2.5 = 3.090169944 a = 3.090169944 Simplifying a = 3.090169944Subproblem 2
a + 2.5 = -5.590169944 Simplifying a + 2.5 = -5.590169944 Reorder the terms: 2.5 + a = -5.590169944 Solving 2.5 + a = -5.590169944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -5.590169944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -5.590169944 + -2.5 a = -5.590169944 + -2.5 Combine like terms: -5.590169944 + -2.5 = -8.090169944 a = -8.090169944 Simplifying a = -8.090169944Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.090169944, -8.090169944}
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