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Simplifying 2x2 + 361x + -64 = 0 Reorder the terms: -64 + 361x + 2x2 = 0 Solving -64 + 361x + 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'. -32 + 180.5x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 180.5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 180.5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 180.5x + x2 = 0 + 32 180.5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 180.5x + x2 = 32 The x term is 180.5x. Take half its coefficient (90.25). Square it (8145.0625) and add it to both sides. Add '8145.0625' to each side of the equation. 180.5x + 8145.0625 + x2 = 32 + 8145.0625 Reorder the terms: 8145.0625 + 180.5x + x2 = 32 + 8145.0625 Combine like terms: 32 + 8145.0625 = 8177.0625 8145.0625 + 180.5x + x2 = 8177.0625 Factor a perfect square on the left side: (x + 90.25)(x + 90.25) = 8177.0625 Calculate the square root of the right side: 90.427111532 Break this problem into two subproblems by setting (x + 90.25) equal to 90.427111532 and -90.427111532.Subproblem 1
x + 90.25 = 90.427111532 Simplifying x + 90.25 = 90.427111532 Reorder the terms: 90.25 + x = 90.427111532 Solving 90.25 + x = 90.427111532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90.25' to each side of the equation. 90.25 + -90.25 + x = 90.427111532 + -90.25 Combine like terms: 90.25 + -90.25 = 0.00 0.00 + x = 90.427111532 + -90.25 x = 90.427111532 + -90.25 Combine like terms: 90.427111532 + -90.25 = 0.177111532 x = 0.177111532 Simplifying x = 0.177111532Subproblem 2
x + 90.25 = -90.427111532 Simplifying x + 90.25 = -90.427111532 Reorder the terms: 90.25 + x = -90.427111532 Solving 90.25 + x = -90.427111532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-90.25' to each side of the equation. 90.25 + -90.25 + x = -90.427111532 + -90.25 Combine like terms: 90.25 + -90.25 = 0.00 0.00 + x = -90.427111532 + -90.25 x = -90.427111532 + -90.25 Combine like terms: -90.427111532 + -90.25 = -180.677111532 x = -180.677111532 Simplifying x = -180.677111532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.177111532, -180.677111532}
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