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Simplifying 16x2 + -40x + 17 = 0 Reorder the terms: 17 + -40x + 16x2 = 0 Solving 17 + -40x + 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 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1.0625' to each side of the equation. 1.0625 + -2.5x + -1.0625 + x2 = 0 + -1.0625 Reorder the terms: 1.0625 + -1.0625 + -2.5x + x2 = 0 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + -2.5x + x2 = 0 + -1.0625 -2.5x + x2 = 0 + -1.0625 Combine like terms: 0 + -1.0625 = -1.0625 -2.5x + x2 = -1.0625 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1.0625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.0625 + 1.5625 Combine like terms: -1.0625 + 1.5625 = 0.5 1.5625 + -2.5x + x2 = 0.5 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -1.25) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -1.25 = 0.707106781 Simplifying x + -1.25 = 0.707106781 Reorder the terms: -1.25 + x = 0.707106781 Solving -1.25 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.707106781 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.707106781 + 1.25 x = 0.707106781 + 1.25 Combine like terms: 0.707106781 + 1.25 = 1.957106781 x = 1.957106781 Simplifying x = 1.957106781Subproblem 2
x + -1.25 = -0.707106781 Simplifying x + -1.25 = -0.707106781 Reorder the terms: -1.25 + x = -0.707106781 Solving -1.25 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.707106781 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.707106781 + 1.25 x = -0.707106781 + 1.25 Combine like terms: -0.707106781 + 1.25 = 0.542893219 x = 0.542893219 Simplifying x = 0.542893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.957106781, 0.542893219}
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