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Simplifying x2 + 35x = 105 Reorder the terms: 35x + x2 = 105 Solving 35x + x2 = 105 Solving for variable 'x'. Reorder the terms: -105 + 35x + x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -105 + 35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 35x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 35x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 35x + x2 = 0 + 105 35x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 35x + x2 = 105 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 = 105 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 105 + 306.25 Combine like terms: 105 + 306.25 = 411.25 306.25 + 35x + x2 = 411.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 411.25 Calculate the square root of the right side: 20.279299791 Break this problem into two subproblems by setting (x + 17.5) equal to 20.279299791 and -20.279299791.Subproblem 1
x + 17.5 = 20.279299791 Simplifying x + 17.5 = 20.279299791 Reorder the terms: 17.5 + x = 20.279299791 Solving 17.5 + x = 20.279299791 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 = 20.279299791 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 20.279299791 + -17.5 x = 20.279299791 + -17.5 Combine like terms: 20.279299791 + -17.5 = 2.779299791 x = 2.779299791 Simplifying x = 2.779299791Subproblem 2
x + 17.5 = -20.279299791 Simplifying x + 17.5 = -20.279299791 Reorder the terms: 17.5 + x = -20.279299791 Solving 17.5 + x = -20.279299791 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 = -20.279299791 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -20.279299791 + -17.5 x = -20.279299791 + -17.5 Combine like terms: -20.279299791 + -17.5 = -37.779299791 x = -37.779299791 Simplifying x = -37.779299791Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.779299791, -37.779299791}
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