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Simplifying 2x2 + 50x + -450 = 0 Reorder the terms: -450 + 50x + 2x2 = 0 Solving -450 + 50x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + 25x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + 25x + x2)' equal to zero and attempt to solve: Simplifying -225 + 25x + x2 = 0 Solving -225 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 25x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 25x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 25x + x2 = 0 + 225 25x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 25x + x2 = 225 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 = 225 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 225 + 156.25 Combine like terms: 225 + 156.25 = 381.25 156.25 + 25x + x2 = 381.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 381.25 Calculate the square root of the right side: 19.52562419 Break this problem into two subproblems by setting (x + 12.5) equal to 19.52562419 and -19.52562419.Subproblem 1
x + 12.5 = 19.52562419 Simplifying x + 12.5 = 19.52562419 Reorder the terms: 12.5 + x = 19.52562419 Solving 12.5 + x = 19.52562419 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 = 19.52562419 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 19.52562419 + -12.5 x = 19.52562419 + -12.5 Combine like terms: 19.52562419 + -12.5 = 7.02562419 x = 7.02562419 Simplifying x = 7.02562419Subproblem 2
x + 12.5 = -19.52562419 Simplifying x + 12.5 = -19.52562419 Reorder the terms: 12.5 + x = -19.52562419 Solving 12.5 + x = -19.52562419 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 = -19.52562419 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -19.52562419 + -12.5 x = -19.52562419 + -12.5 Combine like terms: -19.52562419 + -12.5 = -32.02562419 x = -32.02562419 Simplifying x = -32.02562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.02562419, -32.02562419}Solution
x = {7.02562419, -32.02562419}
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