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Simplifying 16x2 + -5x + -17 = 0 Reorder the terms: -17 + -5x + 16x2 = 0 Solving -17 + -5x + 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'. -1.0625 + -0.3125x + x2 = 0 Move the constant term to the right: Add '1.0625' to each side of the equation. -1.0625 + -0.3125x + 1.0625 + x2 = 0 + 1.0625 Reorder the terms: -1.0625 + 1.0625 + -0.3125x + x2 = 0 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + -0.3125x + x2 = 0 + 1.0625 -0.3125x + x2 = 0 + 1.0625 Combine like terms: 0 + 1.0625 = 1.0625 -0.3125x + x2 = 1.0625 The x term is -0.3125x. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125x + 0.0244140625 + x2 = 1.0625 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125x + x2 = 1.0625 + 0.0244140625 Combine like terms: 1.0625 + 0.0244140625 = 1.0869140625 0.0244140625 + -0.3125x + x2 = 1.0869140625 Factor a perfect square on the left side: (x + -0.15625)(x + -0.15625) = 1.0869140625 Calculate the square root of the right side: 1.042551707 Break this problem into two subproblems by setting (x + -0.15625) equal to 1.042551707 and -1.042551707.Subproblem 1
x + -0.15625 = 1.042551707 Simplifying x + -0.15625 = 1.042551707 Reorder the terms: -0.15625 + x = 1.042551707 Solving -0.15625 + x = 1.042551707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = 1.042551707 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = 1.042551707 + 0.15625 x = 1.042551707 + 0.15625 Combine like terms: 1.042551707 + 0.15625 = 1.198801707 x = 1.198801707 Simplifying x = 1.198801707Subproblem 2
x + -0.15625 = -1.042551707 Simplifying x + -0.15625 = -1.042551707 Reorder the terms: -0.15625 + x = -1.042551707 Solving -0.15625 + x = -1.042551707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + x = -1.042551707 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = -1.042551707 + 0.15625 x = -1.042551707 + 0.15625 Combine like terms: -1.042551707 + 0.15625 = -0.886301707 x = -0.886301707 Simplifying x = -0.886301707Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.198801707, -0.886301707}
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