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Simplifying x2 + 49x + -196 = 0 Reorder the terms: -196 + 49x + x2 = 0 Solving -196 + 49x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 49x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 49x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 49x + x2 = 0 + 196 49x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 49x + x2 = 196 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 = 196 + 600.25 Reorder the terms: 600.25 + 49x + x2 = 196 + 600.25 Combine like terms: 196 + 600.25 = 796.25 600.25 + 49x + x2 = 796.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 796.25 Calculate the square root of the right side: 28.217902119 Break this problem into two subproblems by setting (x + 24.5) equal to 28.217902119 and -28.217902119.Subproblem 1
x + 24.5 = 28.217902119 Simplifying x + 24.5 = 28.217902119 Reorder the terms: 24.5 + x = 28.217902119 Solving 24.5 + x = 28.217902119 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 = 28.217902119 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 28.217902119 + -24.5 x = 28.217902119 + -24.5 Combine like terms: 28.217902119 + -24.5 = 3.717902119 x = 3.717902119 Simplifying x = 3.717902119Subproblem 2
x + 24.5 = -28.217902119 Simplifying x + 24.5 = -28.217902119 Reorder the terms: 24.5 + x = -28.217902119 Solving 24.5 + x = -28.217902119 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 = -28.217902119 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -28.217902119 + -24.5 x = -28.217902119 + -24.5 Combine like terms: -28.217902119 + -24.5 = -52.717902119 x = -52.717902119 Simplifying x = -52.717902119Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.717902119, -52.717902119}
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