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Simplifying x2 + -16x + 11 = 0 Reorder the terms: 11 + -16x + x2 = 0 Solving 11 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -16x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -16x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -16x + x2 = 0 + -11 -16x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -16x + x2 = -11 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -11 + 64 Reorder the terms: 64 + -16x + x2 = -11 + 64 Combine like terms: -11 + 64 = 53 64 + -16x + x2 = 53 Factor a perfect square on the left side: (x + -8)(x + -8) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -8) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -8 = 7.280109889 Simplifying x + -8 = 7.280109889 Reorder the terms: -8 + x = 7.280109889 Solving -8 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.280109889 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.280109889 + 8 x = 7.280109889 + 8 Combine like terms: 7.280109889 + 8 = 15.280109889 x = 15.280109889 Simplifying x = 15.280109889Subproblem 2
x + -8 = -7.280109889 Simplifying x + -8 = -7.280109889 Reorder the terms: -8 + x = -7.280109889 Solving -8 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.280109889 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.280109889 + 8 x = -7.280109889 + 8 Combine like terms: -7.280109889 + 8 = 0.719890111 x = 0.719890111 Simplifying x = 0.719890111Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.280109889, 0.719890111}
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