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Simplifying 2x2 + x + -289 = 0 Reorder the terms: -289 + x + 2x2 = 0 Solving -289 + x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -144.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '144.5' to each side of the equation. -144.5 + 0.5x + 144.5 + x2 = 0 + 144.5 Reorder the terms: -144.5 + 144.5 + 0.5x + x2 = 0 + 144.5 Combine like terms: -144.5 + 144.5 = 0.0 0.0 + 0.5x + x2 = 0 + 144.5 0.5x + x2 = 0 + 144.5 Combine like terms: 0 + 144.5 = 144.5 0.5x + x2 = 144.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 144.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 144.5 + 0.25 Combine like terms: 144.5 + 0.25 = 144.75 0.25 + 0.5x + x2 = 144.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 144.75 Calculate the square root of the right side: 12.031209416 Break this problem into two subproblems by setting (x + 0.5) equal to 12.031209416 and -12.031209416.Subproblem 1
x + 0.5 = 12.031209416 Simplifying x + 0.5 = 12.031209416 Reorder the terms: 0.5 + x = 12.031209416 Solving 0.5 + x = 12.031209416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 12.031209416 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.031209416 + -0.5 x = 12.031209416 + -0.5 Combine like terms: 12.031209416 + -0.5 = 11.531209416 x = 11.531209416 Simplifying x = 11.531209416Subproblem 2
x + 0.5 = -12.031209416 Simplifying x + 0.5 = -12.031209416 Reorder the terms: 0.5 + x = -12.031209416 Solving 0.5 + x = -12.031209416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -12.031209416 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.031209416 + -0.5 x = -12.031209416 + -0.5 Combine like terms: -12.031209416 + -0.5 = -12.531209416 x = -12.531209416 Simplifying x = -12.531209416Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.531209416, -12.531209416}
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