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Simplifying x2 + -16x + 1 = 2 Reorder the terms: 1 + -16x + x2 = 2 Solving 1 + -16x + x2 = 2 Solving for variable 'x'. Reorder the terms: 1 + -2 + -16x + x2 = 2 + -2 Combine like terms: 1 + -2 = -1 -1 + -16x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -1 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -16x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -16x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -16x + x2 = 0 + 1 -16x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -16x + x2 = 1 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 = 1 + 64 Reorder the terms: 64 + -16x + x2 = 1 + 64 Combine like terms: 1 + 64 = 65 64 + -16x + x2 = 65 Factor a perfect square on the left side: (x + -8)(x + -8) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -8) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -8 = 8.062257748 Simplifying x + -8 = 8.062257748 Reorder the terms: -8 + x = 8.062257748 Solving -8 + x = 8.062257748 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 = 8.062257748 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.062257748 + 8 x = 8.062257748 + 8 Combine like terms: 8.062257748 + 8 = 16.062257748 x = 16.062257748 Simplifying x = 16.062257748Subproblem 2
x + -8 = -8.062257748 Simplifying x + -8 = -8.062257748 Reorder the terms: -8 + x = -8.062257748 Solving -8 + x = -8.062257748 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 = -8.062257748 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.062257748 + 8 x = -8.062257748 + 8 Combine like terms: -8.062257748 + 8 = -0.062257748 x = -0.062257748 Simplifying x = -0.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.062257748, -0.062257748}
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