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Simplifying 16x2 + -11x + 1 = 0 Reorder the terms: 1 + -11x + 16x2 = 0 Solving 1 + -11x + 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 + -0.6875x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -0.6875x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -0.6875x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -0.6875x + x2 = 0 + -0.0625 -0.6875x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -0.6875x + x2 = -0.0625 The x term is -0.6875x. Take half its coefficient (-0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. -0.6875x + 0.1181640625 + x2 = -0.0625 + 0.1181640625 Reorder the terms: 0.1181640625 + -0.6875x + x2 = -0.0625 + 0.1181640625 Combine like terms: -0.0625 + 0.1181640625 = 0.0556640625 0.1181640625 + -0.6875x + x2 = 0.0556640625 Factor a perfect square on the left side: (x + -0.34375)(x + -0.34375) = 0.0556640625 Calculate the square root of the right side: 0.235932326 Break this problem into two subproblems by setting (x + -0.34375) equal to 0.235932326 and -0.235932326.Subproblem 1
x + -0.34375 = 0.235932326 Simplifying x + -0.34375 = 0.235932326 Reorder the terms: -0.34375 + x = 0.235932326 Solving -0.34375 + x = 0.235932326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.34375' to each side of the equation. -0.34375 + 0.34375 + x = 0.235932326 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + x = 0.235932326 + 0.34375 x = 0.235932326 + 0.34375 Combine like terms: 0.235932326 + 0.34375 = 0.579682326 x = 0.579682326 Simplifying x = 0.579682326Subproblem 2
x + -0.34375 = -0.235932326 Simplifying x + -0.34375 = -0.235932326 Reorder the terms: -0.34375 + x = -0.235932326 Solving -0.34375 + x = -0.235932326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.34375' to each side of the equation. -0.34375 + 0.34375 + x = -0.235932326 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + x = -0.235932326 + 0.34375 x = -0.235932326 + 0.34375 Combine like terms: -0.235932326 + 0.34375 = 0.107817674 x = 0.107817674 Simplifying x = 0.107817674Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.579682326, 0.107817674}
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