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Simplifying -16x2 + 17x + 1 = 0 Reorder the terms: 1 + 17x + -16x2 = 0 Solving 1 + 17x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.0625 + -1.0625x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -1.0625x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -1.0625x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -1.0625x + x2 = 0 + 0.0625 -1.0625x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -1.0625x + x2 = 0.0625 The x term is -1.0625x. Take half its coefficient (-0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. -1.0625x + 0.2822265625 + x2 = 0.0625 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625x + x2 = 0.0625 + 0.2822265625 Combine like terms: 0.0625 + 0.2822265625 = 0.3447265625 0.2822265625 + -1.0625x + x2 = 0.3447265625 Factor a perfect square on the left side: (x + -0.53125)(x + -0.53125) = 0.3447265625 Calculate the square root of the right side: 0.587134195 Break this problem into two subproblems by setting (x + -0.53125) equal to 0.587134195 and -0.587134195.Subproblem 1
x + -0.53125 = 0.587134195 Simplifying x + -0.53125 = 0.587134195 Reorder the terms: -0.53125 + x = 0.587134195 Solving -0.53125 + x = 0.587134195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + x = 0.587134195 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = 0.587134195 + 0.53125 x = 0.587134195 + 0.53125 Combine like terms: 0.587134195 + 0.53125 = 1.118384195 x = 1.118384195 Simplifying x = 1.118384195Subproblem 2
x + -0.53125 = -0.587134195 Simplifying x + -0.53125 = -0.587134195 Reorder the terms: -0.53125 + x = -0.587134195 Solving -0.53125 + x = -0.587134195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + x = -0.587134195 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = -0.587134195 + 0.53125 x = -0.587134195 + 0.53125 Combine like terms: -0.587134195 + 0.53125 = -0.055884195 x = -0.055884195 Simplifying x = -0.055884195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.118384195, -0.055884195}
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