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Simplifying x2 + 49x + 14 = 11 Reorder the terms: 14 + 49x + x2 = 11 Solving 14 + 49x + x2 = 11 Solving for variable 'x'. Reorder the terms: 14 + -11 + 49x + x2 = 11 + -11 Combine like terms: 14 + -11 = 3 3 + 49x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 3 + 49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 49x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 49x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 49x + x2 = 0 + -3 49x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 49x + x2 = -3 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 = -3 + 600.25 Reorder the terms: 600.25 + 49x + x2 = -3 + 600.25 Combine like terms: -3 + 600.25 = 597.25 600.25 + 49x + x2 = 597.25 Factor a perfect square on the left side: (x + 24.5)(x + 24.5) = 597.25 Calculate the square root of the right side: 24.43869882 Break this problem into two subproblems by setting (x + 24.5) equal to 24.43869882 and -24.43869882.Subproblem 1
x + 24.5 = 24.43869882 Simplifying x + 24.5 = 24.43869882 Reorder the terms: 24.5 + x = 24.43869882 Solving 24.5 + x = 24.43869882 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 = 24.43869882 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 24.43869882 + -24.5 x = 24.43869882 + -24.5 Combine like terms: 24.43869882 + -24.5 = -0.06130118 x = -0.06130118 Simplifying x = -0.06130118Subproblem 2
x + 24.5 = -24.43869882 Simplifying x + 24.5 = -24.43869882 Reorder the terms: 24.5 + x = -24.43869882 Solving 24.5 + x = -24.43869882 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 = -24.43869882 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -24.43869882 + -24.5 x = -24.43869882 + -24.5 Combine like terms: -24.43869882 + -24.5 = -48.93869882 x = -48.93869882 Simplifying x = -48.93869882Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.06130118, -48.93869882}
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