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Simplifying 2x + x2 = 0.051216343 Solving 2x + x2 = 0.051216343 Solving for variable 'x'. Reorder the terms: -0.051216343 + 2x + x2 = 0.051216343 + -0.051216343 Combine like terms: 0.051216343 + -0.051216343 = 0.000000000 -0.051216343 + 2x + x2 = 0.000000000 Begin completing the square. Move the constant term to the right: Add '0.051216343' to each side of the equation. -0.051216343 + 2x + 0.051216343 + x2 = 0.000000000 + 0.051216343 Reorder the terms: -0.051216343 + 0.051216343 + 2x + x2 = 0.000000000 + 0.051216343 Combine like terms: -0.051216343 + 0.051216343 = 0.000000000 0.000000000 + 2x + x2 = 0.000000000 + 0.051216343 2x + x2 = 0.000000000 + 0.051216343 Combine like terms: 0.000000000 + 0.051216343 = 0.051216343 2x + x2 = 0.051216343 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.051216343 + 1 Reorder the terms: 1 + 2x + x2 = 0.051216343 + 1 Combine like terms: 0.051216343 + 1 = 1.051216343 1 + 2x + x2 = 1.051216343 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.051216343 Calculate the square root of the right side: 1.025288419 Break this problem into two subproblems by setting (x + 1) equal to 1.025288419 and -1.025288419.Subproblem 1
x + 1 = 1.025288419 Simplifying x + 1 = 1.025288419 Reorder the terms: 1 + x = 1.025288419 Solving 1 + x = 1.025288419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.025288419 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.025288419 + -1 x = 1.025288419 + -1 Combine like terms: 1.025288419 + -1 = 0.025288419 x = 0.025288419 Simplifying x = 0.025288419Subproblem 2
x + 1 = -1.025288419 Simplifying x + 1 = -1.025288419 Reorder the terms: 1 + x = -1.025288419 Solving 1 + x = -1.025288419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.025288419 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.025288419 + -1 x = -1.025288419 + -1 Combine like terms: -1.025288419 + -1 = -2.025288419 x = -2.025288419 Simplifying x = -2.025288419Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.025288419, -2.025288419}
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