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Simplifying 1 + 17x + -8x2 = 0 Solving 1 + 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'. -0.125 + -2.125x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -2.125x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -2.125x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -2.125x + x2 = 0 + 0.125 -2.125x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -2.125x + x2 = 0.125 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 = 0.125 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 0.125 + 1.12890625 Combine like terms: 0.125 + 1.12890625 = 1.25390625 1.12890625 + -2.125x + x2 = 1.25390625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (x + -1.0625) equal to 1.119779554 and -1.119779554.Subproblem 1
x + -1.0625 = 1.119779554 Simplifying x + -1.0625 = 1.119779554 Reorder the terms: -1.0625 + x = 1.119779554 Solving -1.0625 + x = 1.119779554 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 = 1.119779554 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 1.119779554 + 1.0625 x = 1.119779554 + 1.0625 Combine like terms: 1.119779554 + 1.0625 = 2.182279554 x = 2.182279554 Simplifying x = 2.182279554Subproblem 2
x + -1.0625 = -1.119779554 Simplifying x + -1.0625 = -1.119779554 Reorder the terms: -1.0625 + x = -1.119779554 Solving -1.0625 + x = -1.119779554 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 = -1.119779554 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -1.119779554 + 1.0625 x = -1.119779554 + 1.0625 Combine like terms: -1.119779554 + 1.0625 = -0.057279554 x = -0.057279554 Simplifying x = -0.057279554Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.182279554, -0.057279554}
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