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Simplifying x2 + 35x + 59 = 0 Reorder the terms: 59 + 35x + x2 = 0 Solving 59 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 35x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 35x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 35x + x2 = 0 + -59 35x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 35x + x2 = -59 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 = -59 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -59 + 306.25 Combine like terms: -59 + 306.25 = 247.25 306.25 + 35x + x2 = 247.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 247.25 Calculate the square root of the right side: 15.724185194 Break this problem into two subproblems by setting (x + 17.5) equal to 15.724185194 and -15.724185194.Subproblem 1
x + 17.5 = 15.724185194 Simplifying x + 17.5 = 15.724185194 Reorder the terms: 17.5 + x = 15.724185194 Solving 17.5 + x = 15.724185194 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 = 15.724185194 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 15.724185194 + -17.5 x = 15.724185194 + -17.5 Combine like terms: 15.724185194 + -17.5 = -1.775814806 x = -1.775814806 Simplifying x = -1.775814806Subproblem 2
x + 17.5 = -15.724185194 Simplifying x + 17.5 = -15.724185194 Reorder the terms: 17.5 + x = -15.724185194 Solving 17.5 + x = -15.724185194 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 = -15.724185194 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -15.724185194 + -17.5 x = -15.724185194 + -17.5 Combine like terms: -15.724185194 + -17.5 = -33.224185194 x = -33.224185194 Simplifying x = -33.224185194Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.775814806, -33.224185194}
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