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Simplifying 2x2 + 17x + 37 = x2 + 25 Reorder the terms: 37 + 17x + 2x2 = x2 + 25 Reorder the terms: 37 + 17x + 2x2 = 25 + x2 Solving 37 + 17x + 2x2 = 25 + x2 Solving for variable 'x'. Reorder the terms: 37 + -25 + 17x + 2x2 + -1x2 = 25 + x2 + -25 + -1x2 Combine like terms: 37 + -25 = 12 12 + 17x + 2x2 + -1x2 = 25 + x2 + -25 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 12 + 17x + 1x2 = 25 + x2 + -25 + -1x2 Reorder the terms: 12 + 17x + 1x2 = 25 + -25 + x2 + -1x2 Combine like terms: 25 + -25 = 0 12 + 17x + 1x2 = 0 + x2 + -1x2 12 + 17x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12 + 17x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 17x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 17x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 17x + x2 = 0 + -12 17x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 17x + x2 = -12 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -12 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -12 + 72.25 Combine like terms: -12 + 72.25 = 60.25 72.25 + 17x + x2 = 60.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x + 8.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x + 8.5 = 7.762087348 Simplifying x + 8.5 = 7.762087348 Reorder the terms: 8.5 + x = 7.762087348 Solving 8.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 7.762087348 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 7.762087348 + -8.5 x = 7.762087348 + -8.5 Combine like terms: 7.762087348 + -8.5 = -0.737912652 x = -0.737912652 Simplifying x = -0.737912652Subproblem 2
x + 8.5 = -7.762087348 Simplifying x + 8.5 = -7.762087348 Reorder the terms: 8.5 + x = -7.762087348 Solving 8.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -7.762087348 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -7.762087348 + -8.5 x = -7.762087348 + -8.5 Combine like terms: -7.762087348 + -8.5 = -16.262087348 x = -16.262087348 Simplifying x = -16.262087348Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.737912652, -16.262087348}
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