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Simplifying x = -2x2 + 6x + 2 Reorder the terms: x = 2 + 6x + -2x2 Solving x = 2 + 6x + -2x2 Solving for variable 'x'. Reorder the terms: -2 + x + -6x + 2x2 = 2 + 6x + -2x2 + -2 + -6x + 2x2 Combine like terms: x + -6x = -5x -2 + -5x + 2x2 = 2 + 6x + -2x2 + -2 + -6x + 2x2 Reorder the terms: -2 + -5x + 2x2 = 2 + -2 + 6x + -6x + -2x2 + 2x2 Combine like terms: 2 + -2 = 0 -2 + -5x + 2x2 = 0 + 6x + -6x + -2x2 + 2x2 -2 + -5x + 2x2 = 6x + -6x + -2x2 + 2x2 Combine like terms: 6x + -6x = 0 -2 + -5x + 2x2 = 0 + -2x2 + 2x2 -2 + -5x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -2 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -2.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.5x + x2 = 0 + 1 -2.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.5x + x2 = 1 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 1 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 1 + 1.5625 Combine like terms: 1 + 1.5625 = 2.5625 1.5625 + -2.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -1.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -1.25 = 1.600781059 Simplifying x + -1.25 = 1.600781059 Reorder the terms: -1.25 + x = 1.600781059 Solving -1.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.600781059 + 1.25 x = 1.600781059 + 1.25 Combine like terms: 1.600781059 + 1.25 = 2.850781059 x = 2.850781059 Simplifying x = 2.850781059Subproblem 2
x + -1.25 = -1.600781059 Simplifying x + -1.25 = -1.600781059 Reorder the terms: -1.25 + x = -1.600781059 Solving -1.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.600781059 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.600781059 + 1.25 x = -1.600781059 + 1.25 Combine like terms: -1.600781059 + 1.25 = -0.350781059 x = -0.350781059 Simplifying x = -0.350781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.850781059, -0.350781059}
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