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Simplifying 2x2 + -14x + -49 = x2 + 2x + 1 Reorder the terms: -49 + -14x + 2x2 = x2 + 2x + 1 Reorder the terms: -49 + -14x + 2x2 = 1 + 2x + x2 Solving -49 + -14x + 2x2 = 1 + 2x + x2 Solving for variable 'x'. Reorder the terms: -49 + -1 + -14x + -2x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Combine like terms: -49 + -1 = -50 -50 + -14x + -2x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Combine like terms: -14x + -2x = -16x -50 + -16x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -50 + -16x + 1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Reorder the terms: -50 + -16x + 1x2 = 1 + -1 + 2x + -2x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -50 + -16x + 1x2 = 0 + 2x + -2x + x2 + -1x2 -50 + -16x + 1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -50 + -16x + 1x2 = 0 + x2 + -1x2 -50 + -16x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + -16x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -16x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -16x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -16x + x2 = 0 + 50 -16x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -16x + x2 = 50 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 50 + 64 Reorder the terms: 64 + -16x + x2 = 50 + 64 Combine like terms: 50 + 64 = 114 64 + -16x + x2 = 114 Factor a perfect square on the left side: (x + -8)(x + -8) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + -8) equal to 10.677078252 and -10.677078252.Subproblem 1
x + -8 = 10.677078252 Simplifying x + -8 = 10.677078252 Reorder the terms: -8 + x = 10.677078252 Solving -8 + x = 10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 10.677078252 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.677078252 + 8 x = 10.677078252 + 8 Combine like terms: 10.677078252 + 8 = 18.677078252 x = 18.677078252 Simplifying x = 18.677078252Subproblem 2
x + -8 = -10.677078252 Simplifying x + -8 = -10.677078252 Reorder the terms: -8 + x = -10.677078252 Solving -8 + x = -10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -10.677078252 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.677078252 + 8 x = -10.677078252 + 8 Combine like terms: -10.677078252 + 8 = -2.677078252 x = -2.677078252 Simplifying x = -2.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.677078252, -2.677078252}
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