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Simplifying 16x2 + -8x + 1 = 20 Reorder the terms: 1 + -8x + 16x2 = 20 Solving 1 + -8x + 16x2 = 20 Solving for variable 'x'. Reorder the terms: 1 + -20 + -8x + 16x2 = 20 + -20 Combine like terms: 1 + -20 = -19 -19 + -8x + 16x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -19 + -8x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.1875 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.1875' to each side of the equation. -1.1875 + -0.5x + 1.1875 + x2 = 0 + 1.1875 Reorder the terms: -1.1875 + 1.1875 + -0.5x + x2 = 0 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + -0.5x + x2 = 0 + 1.1875 -0.5x + x2 = 0 + 1.1875 Combine like terms: 0 + 1.1875 = 1.1875 -0.5x + x2 = 1.1875 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.1875 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.1875 + 0.0625 Combine like terms: 1.1875 + 0.0625 = 1.25 0.0625 + -0.5x + x2 = 1.25 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -0.25) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -0.25 = 1.118033989 Simplifying x + -0.25 = 1.118033989 Reorder the terms: -0.25 + x = 1.118033989 Solving -0.25 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.118033989 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.118033989 + 0.25 x = 1.118033989 + 0.25 Combine like terms: 1.118033989 + 0.25 = 1.368033989 x = 1.368033989 Simplifying x = 1.368033989Subproblem 2
x + -0.25 = -1.118033989 Simplifying x + -0.25 = -1.118033989 Reorder the terms: -0.25 + x = -1.118033989 Solving -0.25 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.118033989 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.118033989 + 0.25 x = -1.118033989 + 0.25 Combine like terms: -1.118033989 + 0.25 = -0.868033989 x = -0.868033989 Simplifying x = -0.868033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.368033989, -0.868033989}
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