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Simplifying x2 + 25x + 53 = 0 Reorder the terms: 53 + 25x + x2 = 0 Solving 53 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 25x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 25x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 25x + x2 = 0 + -53 25x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 25x + x2 = -53 The x term is 25x. 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. 25x + 156.25 + x2 = -53 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -53 + 156.25 Combine like terms: -53 + 156.25 = 103.25 156.25 + 25x + x2 = 103.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 103.25 Calculate the square root of the right side: 10.161200716 Break this problem into two subproblems by setting (x + 12.5) equal to 10.161200716 and -10.161200716.Subproblem 1
x + 12.5 = 10.161200716 Simplifying x + 12.5 = 10.161200716 Reorder the terms: 12.5 + x = 10.161200716 Solving 12.5 + x = 10.161200716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 10.161200716 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 10.161200716 + -12.5 x = 10.161200716 + -12.5 Combine like terms: 10.161200716 + -12.5 = -2.338799284 x = -2.338799284 Simplifying x = -2.338799284Subproblem 2
x + 12.5 = -10.161200716 Simplifying x + 12.5 = -10.161200716 Reorder the terms: 12.5 + x = -10.161200716 Solving 12.5 + x = -10.161200716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -10.161200716 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -10.161200716 + -12.5 x = -10.161200716 + -12.5 Combine like terms: -10.161200716 + -12.5 = -22.661200716 x = -22.661200716 Simplifying x = -22.661200716Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.338799284, -22.661200716}
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