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Simplifying (8x2 + y2 + -6) + -1(6x2 + y2 + -2) = x Reorder the terms: (-6 + 8x2 + y2) + -1(6x2 + y2 + -2) = x Remove parenthesis around (-6 + 8x2 + y2) -6 + 8x2 + y2 + -1(6x2 + y2 + -2) = x Reorder the terms: -6 + 8x2 + y2 + -1(-2 + 6x2 + y2) = x -6 + 8x2 + y2 + (-2 * -1 + 6x2 * -1 + y2 * -1) = x -6 + 8x2 + y2 + (2 + -6x2 + -1y2) = x Reorder the terms: -6 + 2 + 8x2 + -6x2 + y2 + -1y2 = x Combine like terms: -6 + 2 = -4 -4 + 8x2 + -6x2 + y2 + -1y2 = x Combine like terms: 8x2 + -6x2 = 2x2 -4 + 2x2 + y2 + -1y2 = x Combine like terms: y2 + -1y2 = 0 -4 + 2x2 + 0 = x -4 + 2x2 = x Solving -4 + 2x2 = x Solving for variable 'x'. Reorder the terms: -4 + -1x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -4 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -0.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.5x + x2 = 0 + 2 -0.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.5x + x2 = 2 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 2 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 2 + 0.0625 Combine like terms: 2 + 0.0625 = 2.0625 0.0625 + -0.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + -0.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x + -0.25 = 1.436140662 Simplifying x + -0.25 = 1.436140662 Reorder the terms: -0.25 + x = 1.436140662 Solving -0.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.436140662 + 0.25 x = 1.436140662 + 0.25 Combine like terms: 1.436140662 + 0.25 = 1.686140662 x = 1.686140662 Simplifying x = 1.686140662Subproblem 2
x + -0.25 = -1.436140662 Simplifying x + -0.25 = -1.436140662 Reorder the terms: -0.25 + x = -1.436140662 Solving -0.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.436140662 + 0.25 x = -1.436140662 + 0.25 Combine like terms: -1.436140662 + 0.25 = -1.186140662 x = -1.186140662 Simplifying x = -1.186140662Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.686140662, -1.186140662}
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