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Simplifying x2 + 35x + -2 = 0 Reorder the terms: -2 + 35x + x2 = 0 Solving -2 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 35x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 35x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 35x + x2 = 0 + 2 35x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 35x + x2 = 2 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 2 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 2 + 306.25 Combine like terms: 2 + 306.25 = 308.25 306.25 + 35x + x2 = 308.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 308.25 Calculate the square root of the right side: 17.557049866 Break this problem into two subproblems by setting (x + 17.5) equal to 17.557049866 and -17.557049866.Subproblem 1
x + 17.5 = 17.557049866 Simplifying x + 17.5 = 17.557049866 Reorder the terms: 17.5 + x = 17.557049866 Solving 17.5 + x = 17.557049866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 17.557049866 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 17.557049866 + -17.5 x = 17.557049866 + -17.5 Combine like terms: 17.557049866 + -17.5 = 0.057049866 x = 0.057049866 Simplifying x = 0.057049866Subproblem 2
x + 17.5 = -17.557049866 Simplifying x + 17.5 = -17.557049866 Reorder the terms: 17.5 + x = -17.557049866 Solving 17.5 + x = -17.557049866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -17.557049866 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -17.557049866 + -17.5 x = -17.557049866 + -17.5 Combine like terms: -17.557049866 + -17.5 = -35.057049866 x = -35.057049866 Simplifying x = -35.057049866Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.057049866, -35.057049866}
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