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Simplifying x2 + 35x + 11 = 0 Reorder the terms: 11 + 35x + x2 = 0 Solving 11 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 35x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 35x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 35x + x2 = 0 + -11 35x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 35x + x2 = -11 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 = -11 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -11 + 306.25 Combine like terms: -11 + 306.25 = 295.25 306.25 + 35x + x2 = 295.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 295.25 Calculate the square root of the right side: 17.182840277 Break this problem into two subproblems by setting (x + 17.5) equal to 17.182840277 and -17.182840277.Subproblem 1
x + 17.5 = 17.182840277 Simplifying x + 17.5 = 17.182840277 Reorder the terms: 17.5 + x = 17.182840277 Solving 17.5 + x = 17.182840277 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 = 17.182840277 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 17.182840277 + -17.5 x = 17.182840277 + -17.5 Combine like terms: 17.182840277 + -17.5 = -0.317159723 x = -0.317159723 Simplifying x = -0.317159723Subproblem 2
x + 17.5 = -17.182840277 Simplifying x + 17.5 = -17.182840277 Reorder the terms: 17.5 + x = -17.182840277 Solving 17.5 + x = -17.182840277 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 = -17.182840277 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -17.182840277 + -17.5 x = -17.182840277 + -17.5 Combine like terms: -17.182840277 + -17.5 = -34.682840277 x = -34.682840277 Simplifying x = -34.682840277Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.317159723, -34.682840277}
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