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Simplifying -16x2 + 20x + 1 = 0 Reorder the terms: 1 + 20x + -16x2 = 0 Solving 1 + 20x + -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'. -0.0625 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -1.25x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -1.25x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -1.25x + x2 = 0 + 0.0625 -1.25x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -1.25x + x2 = 0.0625 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 0.0625 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.0625 + 0.390625 Combine like terms: 0.0625 + 0.390625 = 0.453125 0.390625 + -1.25x + x2 = 0.453125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.453125 Calculate the square root of the right side: 0.673145601 Break this problem into two subproblems by setting (x + -0.625) equal to 0.673145601 and -0.673145601.Subproblem 1
x + -0.625 = 0.673145601 Simplifying x + -0.625 = 0.673145601 Reorder the terms: -0.625 + x = 0.673145601 Solving -0.625 + x = 0.673145601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.673145601 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.673145601 + 0.625 x = 0.673145601 + 0.625 Combine like terms: 0.673145601 + 0.625 = 1.298145601 x = 1.298145601 Simplifying x = 1.298145601Subproblem 2
x + -0.625 = -0.673145601 Simplifying x + -0.625 = -0.673145601 Reorder the terms: -0.625 + x = -0.673145601 Solving -0.625 + x = -0.673145601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.673145601 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.673145601 + 0.625 x = -0.673145601 + 0.625 Combine like terms: -0.673145601 + 0.625 = -0.048145601 x = -0.048145601 Simplifying x = -0.048145601Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.298145601, -0.048145601}
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