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Simplifying 2x2 + 16x + 1 = 0 Reorder the terms: 1 + 16x + 2x2 = 0 Solving 1 + 16x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 8x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 8x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 8x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 8x + x2 = 0 + -0.5 8x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 8x + x2 = -0.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -0.5 + 16 Reorder the terms: 16 + 8x + x2 = -0.5 + 16 Combine like terms: -0.5 + 16 = 15.5 16 + 8x + x2 = 15.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 15.5 Calculate the square root of the right side: 3.937003937 Break this problem into two subproblems by setting (x + 4) equal to 3.937003937 and -3.937003937.Subproblem 1
x + 4 = 3.937003937 Simplifying x + 4 = 3.937003937 Reorder the terms: 4 + x = 3.937003937 Solving 4 + x = 3.937003937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.937003937 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.937003937 + -4 x = 3.937003937 + -4 Combine like terms: 3.937003937 + -4 = -0.062996063 x = -0.062996063 Simplifying x = -0.062996063Subproblem 2
x + 4 = -3.937003937 Simplifying x + 4 = -3.937003937 Reorder the terms: 4 + x = -3.937003937 Solving 4 + x = -3.937003937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.937003937 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.937003937 + -4 x = -3.937003937 + -4 Combine like terms: -3.937003937 + -4 = -7.937003937 x = -7.937003937 Simplifying x = -7.937003937Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.062996063, -7.937003937}
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