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Simplifying x2 + 50x + 30 = 0 Reorder the terms: 30 + 50x + x2 = 0 Solving 30 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 50x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 50x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 50x + x2 = 0 + -30 50x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 50x + x2 = -30 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = -30 + 625 Reorder the terms: 625 + 50x + x2 = -30 + 625 Combine like terms: -30 + 625 = 595 625 + 50x + x2 = 595 Factor a perfect square on the left side: (x + 25)(x + 25) = 595 Calculate the square root of the right side: 24.392621835 Break this problem into two subproblems by setting (x + 25) equal to 24.392621835 and -24.392621835.Subproblem 1
x + 25 = 24.392621835 Simplifying x + 25 = 24.392621835 Reorder the terms: 25 + x = 24.392621835 Solving 25 + x = 24.392621835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 24.392621835 + -25 Combine like terms: 25 + -25 = 0 0 + x = 24.392621835 + -25 x = 24.392621835 + -25 Combine like terms: 24.392621835 + -25 = -0.607378165 x = -0.607378165 Simplifying x = -0.607378165Subproblem 2
x + 25 = -24.392621835 Simplifying x + 25 = -24.392621835 Reorder the terms: 25 + x = -24.392621835 Solving 25 + x = -24.392621835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -24.392621835 + -25 Combine like terms: 25 + -25 = 0 0 + x = -24.392621835 + -25 x = -24.392621835 + -25 Combine like terms: -24.392621835 + -25 = -49.392621835 x = -49.392621835 Simplifying x = -49.392621835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.607378165, -49.392621835}
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