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Simplifying 2x2 + -7x + -97 = 0 Reorder the terms: -97 + -7x + 2x2 = 0 Solving -97 + -7x + 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'. -48.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '48.5' to each side of the equation. -48.5 + -3.5x + 48.5 + x2 = 0 + 48.5 Reorder the terms: -48.5 + 48.5 + -3.5x + x2 = 0 + 48.5 Combine like terms: -48.5 + 48.5 = 0.0 0.0 + -3.5x + x2 = 0 + 48.5 -3.5x + x2 = 0 + 48.5 Combine like terms: 0 + 48.5 = 48.5 -3.5x + x2 = 48.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 48.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 48.5 + 3.0625 Combine like terms: 48.5 + 3.0625 = 51.5625 3.0625 + -3.5x + x2 = 51.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (x + -1.75) equal to 7.180703308 and -7.180703308.Subproblem 1
x + -1.75 = 7.180703308 Simplifying x + -1.75 = 7.180703308 Reorder the terms: -1.75 + x = 7.180703308 Solving -1.75 + x = 7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 7.180703308 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 7.180703308 + 1.75 x = 7.180703308 + 1.75 Combine like terms: 7.180703308 + 1.75 = 8.930703308 x = 8.930703308 Simplifying x = 8.930703308Subproblem 2
x + -1.75 = -7.180703308 Simplifying x + -1.75 = -7.180703308 Reorder the terms: -1.75 + x = -7.180703308 Solving -1.75 + x = -7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -7.180703308 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -7.180703308 + 1.75 x = -7.180703308 + 1.75 Combine like terms: -7.180703308 + 1.75 = -5.430703308 x = -5.430703308 Simplifying x = -5.430703308Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.930703308, -5.430703308}
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