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Simplifying x2 + 35x + 305 = 0 Reorder the terms: 305 + 35x + x2 = 0 Solving 305 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-305' to each side of the equation. 305 + 35x + -305 + x2 = 0 + -305 Reorder the terms: 305 + -305 + 35x + x2 = 0 + -305 Combine like terms: 305 + -305 = 0 0 + 35x + x2 = 0 + -305 35x + x2 = 0 + -305 Combine like terms: 0 + -305 = -305 35x + x2 = -305 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 = -305 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -305 + 306.25 Combine like terms: -305 + 306.25 = 1.25 306.25 + 35x + x2 = 1.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 17.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 17.5 = 1.118033989 Simplifying x + 17.5 = 1.118033989 Reorder the terms: 17.5 + x = 1.118033989 Solving 17.5 + x = 1.118033989 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 = 1.118033989 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 1.118033989 + -17.5 x = 1.118033989 + -17.5 Combine like terms: 1.118033989 + -17.5 = -16.381966011 x = -16.381966011 Simplifying x = -16.381966011Subproblem 2
x + 17.5 = -1.118033989 Simplifying x + 17.5 = -1.118033989 Reorder the terms: 17.5 + x = -1.118033989 Solving 17.5 + x = -1.118033989 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 = -1.118033989 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -1.118033989 + -17.5 x = -1.118033989 + -17.5 Combine like terms: -1.118033989 + -17.5 = -18.618033989 x = -18.618033989 Simplifying x = -18.618033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-16.381966011, -18.618033989}
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