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Simplifying 2x2 + x + -349 = 0 Reorder the terms: -349 + x + 2x2 = 0 Solving -349 + 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'. -174.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '174.5' to each side of the equation. -174.5 + 0.5x + 174.5 + x2 = 0 + 174.5 Reorder the terms: -174.5 + 174.5 + 0.5x + x2 = 0 + 174.5 Combine like terms: -174.5 + 174.5 = 0.0 0.0 + 0.5x + x2 = 0 + 174.5 0.5x + x2 = 0 + 174.5 Combine like terms: 0 + 174.5 = 174.5 0.5x + x2 = 174.5 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 = 174.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 174.5 + 0.25 Combine like terms: 174.5 + 0.25 = 174.75 0.25 + 0.5x + x2 = 174.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 174.75 Calculate the square root of the right side: 13.219304066 Break this problem into two subproblems by setting (x + 0.5) equal to 13.219304066 and -13.219304066.Subproblem 1
x + 0.5 = 13.219304066 Simplifying x + 0.5 = 13.219304066 Reorder the terms: 0.5 + x = 13.219304066 Solving 0.5 + x = 13.219304066 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 = 13.219304066 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 13.219304066 + -0.5 x = 13.219304066 + -0.5 Combine like terms: 13.219304066 + -0.5 = 12.719304066 x = 12.719304066 Simplifying x = 12.719304066Subproblem 2
x + 0.5 = -13.219304066 Simplifying x + 0.5 = -13.219304066 Reorder the terms: 0.5 + x = -13.219304066 Solving 0.5 + x = -13.219304066 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 = -13.219304066 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -13.219304066 + -0.5 x = -13.219304066 + -0.5 Combine like terms: -13.219304066 + -0.5 = -13.719304066 x = -13.719304066 Simplifying x = -13.719304066Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.719304066, -13.719304066}
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