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Simplifying 2x2 + 50x + -2 = 0 Reorder the terms: -2 + 50x + 2x2 = 0 Solving -2 + 50x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 25x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 25x + x2)' equal to zero and attempt to solve: Simplifying -1 + 25x + x2 = 0 Solving -1 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 25x + x2 = 0 + 1 25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 25x + x2 = 1 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 = 1 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 1 + 156.25 Combine like terms: 1 + 156.25 = 157.25 156.25 + 25x + x2 = 157.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 157.25 Calculate the square root of the right side: 12.539936204 Break this problem into two subproblems by setting (x + 12.5) equal to 12.539936204 and -12.539936204.Subproblem 1
x + 12.5 = 12.539936204 Simplifying x + 12.5 = 12.539936204 Reorder the terms: 12.5 + x = 12.539936204 Solving 12.5 + x = 12.539936204 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 = 12.539936204 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.539936204 + -12.5 x = 12.539936204 + -12.5 Combine like terms: 12.539936204 + -12.5 = 0.039936204 x = 0.039936204 Simplifying x = 0.039936204Subproblem 2
x + 12.5 = -12.539936204 Simplifying x + 12.5 = -12.539936204 Reorder the terms: 12.5 + x = -12.539936204 Solving 12.5 + x = -12.539936204 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 = -12.539936204 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.539936204 + -12.5 x = -12.539936204 + -12.5 Combine like terms: -12.539936204 + -12.5 = -25.039936204 x = -25.039936204 Simplifying x = -25.039936204Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.039936204, -25.039936204}Solution
x = {0.039936204, -25.039936204}
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