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Simplifying -16x2 + 50x + 1 = 0 Reorder the terms: 1 + 50x + -16x2 = 0 Solving 1 + 50x + -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 + -3.125x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -3.125x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -3.125x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -3.125x + x2 = 0 + 0.0625 -3.125x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -3.125x + x2 = 0.0625 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 0.0625 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 0.0625 + 2.44140625 Combine like terms: 0.0625 + 2.44140625 = 2.50390625 2.44140625 + -3.125x + x2 = 2.50390625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.50390625 Calculate the square root of the right side: 1.582373613 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.582373613 and -1.582373613.Subproblem 1
x + -1.5625 = 1.582373613 Simplifying x + -1.5625 = 1.582373613 Reorder the terms: -1.5625 + x = 1.582373613 Solving -1.5625 + x = 1.582373613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.582373613 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.582373613 + 1.5625 x = 1.582373613 + 1.5625 Combine like terms: 1.582373613 + 1.5625 = 3.144873613 x = 3.144873613 Simplifying x = 3.144873613Subproblem 2
x + -1.5625 = -1.582373613 Simplifying x + -1.5625 = -1.582373613 Reorder the terms: -1.5625 + x = -1.582373613 Solving -1.5625 + x = -1.582373613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.582373613 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.582373613 + 1.5625 x = -1.582373613 + 1.5625 Combine like terms: -1.582373613 + 1.5625 = -0.019873613 x = -0.019873613 Simplifying x = -0.019873613Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.144873613, -0.019873613}
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