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Simplifying -2 + -16x + -1x + 8x2 = 0 Combine like terms: -16x + -1x = -17x -2 + -17x + 8x2 = 0 Solving -2 + -17x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -2.125x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.125x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.125x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.125x + x2 = 0 + 0.25 -2.125x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.125x + x2 = 0.25 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = 0.25 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 0.25 + 1.12890625 Combine like terms: 0.25 + 1.12890625 = 1.37890625 1.12890625 + -2.125x + x2 = 1.37890625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 1.37890625 Calculate the square root of the right side: 1.174268389 Break this problem into two subproblems by setting (x + -1.0625) equal to 1.174268389 and -1.174268389.Subproblem 1
x + -1.0625 = 1.174268389 Simplifying x + -1.0625 = 1.174268389 Reorder the terms: -1.0625 + x = 1.174268389 Solving -1.0625 + x = 1.174268389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 1.174268389 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 1.174268389 + 1.0625 x = 1.174268389 + 1.0625 Combine like terms: 1.174268389 + 1.0625 = 2.236768389 x = 2.236768389 Simplifying x = 2.236768389Subproblem 2
x + -1.0625 = -1.174268389 Simplifying x + -1.0625 = -1.174268389 Reorder the terms: -1.0625 + x = -1.174268389 Solving -1.0625 + x = -1.174268389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -1.174268389 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -1.174268389 + 1.0625 x = -1.174268389 + 1.0625 Combine like terms: -1.174268389 + 1.0625 = -0.111768389 x = -0.111768389 Simplifying x = -0.111768389Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.236768389, -0.111768389}
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