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Simplifying x2 + 49x + 35 = 0 Reorder the terms: 35 + 49x + x2 = 0 Solving 35 + 49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 49x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 49x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 49x + x2 = 0 + -35 49x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 49x + x2 = -35 The x term is 49x. Take half its coefficient (24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. 49x + 600.25 + x2 = -35 + 600.25 Reorder the terms: 600.25 + 49x + x2 = -35 + 600.25 Combine like terms: -35 + 600.25 = 565.25 600.25 + 49x + x2 = 565.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 565.25 Calculate the square root of the right side: 23.774986856 Break this problem into two subproblems by setting (x + 24.5) equal to 23.774986856 and -23.774986856.Subproblem 1
x + 24.5 = 23.774986856 Simplifying x + 24.5 = 23.774986856 Reorder the terms: 24.5 + x = 23.774986856 Solving 24.5 + x = 23.774986856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 23.774986856 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 23.774986856 + -24.5 x = 23.774986856 + -24.5 Combine like terms: 23.774986856 + -24.5 = -0.725013144 x = -0.725013144 Simplifying x = -0.725013144Subproblem 2
x + 24.5 = -23.774986856 Simplifying x + 24.5 = -23.774986856 Reorder the terms: 24.5 + x = -23.774986856 Solving 24.5 + x = -23.774986856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -23.774986856 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -23.774986856 + -24.5 x = -23.774986856 + -24.5 Combine like terms: -23.774986856 + -24.5 = -48.274986856 x = -48.274986856 Simplifying x = -48.274986856Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.725013144, -48.274986856}
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