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Simplifying -168 + -122x = -32x2 + x Reorder the terms: -168 + -122x = x + -32x2 Solving -168 + -122x = x + -32x2 Solving for variable 'x'. Combine like terms: -122x + -1x = -123x -168 + -123x + 32x2 = x + -32x2 + -1x + 32x2 Reorder the terms: -168 + -123x + 32x2 = x + -1x + -32x2 + 32x2 Combine like terms: x + -1x = 0 -168 + -123x + 32x2 = 0 + -32x2 + 32x2 -168 + -123x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 -168 + -123x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -5.25 + -3.84375x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -3.84375x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -3.84375x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -3.84375x + x2 = 0 + 5.25 -3.84375x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -3.84375x + x2 = 5.25 The x term is -3.84375x. Take half its coefficient (-1.921875). Square it (3.693603516) and add it to both sides. Add '3.693603516' to each side of the equation. -3.84375x + 3.693603516 + x2 = 5.25 + 3.693603516 Reorder the terms: 3.693603516 + -3.84375x + x2 = 5.25 + 3.693603516 Combine like terms: 5.25 + 3.693603516 = 8.943603516 3.693603516 + -3.84375x + x2 = 8.943603516 Factor a perfect square on the left side: (x + -1.921875)(x + -1.921875) = 8.943603516 Calculate the square root of the right side: 2.990585815 Break this problem into two subproblems by setting (x + -1.921875) equal to 2.990585815 and -2.990585815.Subproblem 1
x + -1.921875 = 2.990585815 Simplifying x + -1.921875 = 2.990585815 Reorder the terms: -1.921875 + x = 2.990585815 Solving -1.921875 + x = 2.990585815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.921875' to each side of the equation. -1.921875 + 1.921875 + x = 2.990585815 + 1.921875 Combine like terms: -1.921875 + 1.921875 = 0.000000 0.000000 + x = 2.990585815 + 1.921875 x = 2.990585815 + 1.921875 Combine like terms: 2.990585815 + 1.921875 = 4.912460815 x = 4.912460815 Simplifying x = 4.912460815Subproblem 2
x + -1.921875 = -2.990585815 Simplifying x + -1.921875 = -2.990585815 Reorder the terms: -1.921875 + x = -2.990585815 Solving -1.921875 + x = -2.990585815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.921875' to each side of the equation. -1.921875 + 1.921875 + x = -2.990585815 + 1.921875 Combine like terms: -1.921875 + 1.921875 = 0.000000 0.000000 + x = -2.990585815 + 1.921875 x = -2.990585815 + 1.921875 Combine like terms: -2.990585815 + 1.921875 = -1.068710815 x = -1.068710815 Simplifying x = -1.068710815Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.912460815, -1.068710815}
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