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Simplifying 2X2 + 25X + 50 + -1X2 + 2X + 1 = 0 Reorder the terms: 50 + 1 + 25X + 2X + 2X2 + -1X2 = 0 Combine like terms: 50 + 1 = 51 51 + 25X + 2X + 2X2 + -1X2 = 0 Combine like terms: 25X + 2X = 27X 51 + 27X + 2X2 + -1X2 = 0 Combine like terms: 2X2 + -1X2 = 1X2 51 + 27X + 1X2 = 0 Solving 51 + 27X + 1X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + 27X + -51 + X2 = 0 + -51 Reorder the terms: 51 + -51 + 27X + X2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + 27X + X2 = 0 + -51 27X + X2 = 0 + -51 Combine like terms: 0 + -51 = -51 27X + X2 = -51 The X term is 27X. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27X + 182.25 + X2 = -51 + 182.25 Reorder the terms: 182.25 + 27X + X2 = -51 + 182.25 Combine like terms: -51 + 182.25 = 131.25 182.25 + 27X + X2 = 131.25 Factor a perfect square on the left side: (X + 13.5)(X + 13.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (X + 13.5) equal to 11.456439237 and -11.456439237.Subproblem 1
X + 13.5 = 11.456439237 Simplifying X + 13.5 = 11.456439237 Reorder the terms: 13.5 + X = 11.456439237 Solving 13.5 + X = 11.456439237 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + X = 11.456439237 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + X = 11.456439237 + -13.5 X = 11.456439237 + -13.5 Combine like terms: 11.456439237 + -13.5 = -2.043560763 X = -2.043560763 Simplifying X = -2.043560763Subproblem 2
X + 13.5 = -11.456439237 Simplifying X + 13.5 = -11.456439237 Reorder the terms: 13.5 + X = -11.456439237 Solving 13.5 + X = -11.456439237 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + X = -11.456439237 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + X = -11.456439237 + -13.5 X = -11.456439237 + -13.5 Combine like terms: -11.456439237 + -13.5 = -24.956439237 X = -24.956439237 Simplifying X = -24.956439237Solution
The solution to the problem is based on the solutions from the subproblems. X = {-2.043560763, -24.956439237}
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