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Simplifying (2x + -1) * x + -16 = 0 Reorder the terms: (-1 + 2x) * x + -16 = 0 Reorder the terms for easier multiplication: x(-1 + 2x) + -16 = 0 (-1 * x + 2x * x) + -16 = 0 (-1x + 2x2) + -16 = 0 Reorder the terms: -16 + -1x + 2x2 = 0 Solving -16 + -1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -0.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -0.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.5x + x2 = 0 + 8 -0.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.5x + x2 = 8 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 = 8 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 8 + 0.0625 Combine like terms: 8 + 0.0625 = 8.0625 0.0625 + -0.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -0.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -0.25 = 2.839454173 Simplifying x + -0.25 = 2.839454173 Reorder the terms: -0.25 + x = 2.839454173 Solving -0.25 + x = 2.839454173 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 = 2.839454173 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.839454173 + 0.25 x = 2.839454173 + 0.25 Combine like terms: 2.839454173 + 0.25 = 3.089454173 x = 3.089454173 Simplifying x = 3.089454173Subproblem 2
x + -0.25 = -2.839454173 Simplifying x + -0.25 = -2.839454173 Reorder the terms: -0.25 + x = -2.839454173 Solving -0.25 + x = -2.839454173 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 = -2.839454173 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.839454173 + 0.25 x = -2.839454173 + 0.25 Combine like terms: -2.839454173 + 0.25 = -2.589454173 x = -2.589454173 Simplifying x = -2.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.089454173, -2.589454173}
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