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Simplifying 16x2 + -2x + -47 = 0 Reorder the terms: -47 + -2x + 16x2 = 0 Solving -47 + -2x + 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'. -2.9375 + -0.125x + x2 = 0 Move the constant term to the right: Add '2.9375' to each side of the equation. -2.9375 + -0.125x + 2.9375 + x2 = 0 + 2.9375 Reorder the terms: -2.9375 + 2.9375 + -0.125x + x2 = 0 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + -0.125x + x2 = 0 + 2.9375 -0.125x + x2 = 0 + 2.9375 Combine like terms: 0 + 2.9375 = 2.9375 -0.125x + x2 = 2.9375 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 2.9375 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 2.9375 + 0.00390625 Combine like terms: 2.9375 + 0.00390625 = 2.94140625 0.00390625 + -0.125x + x2 = 2.94140625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 2.94140625 Calculate the square root of the right side: 1.715052842 Break this problem into two subproblems by setting (x + -0.0625) equal to 1.715052842 and -1.715052842.Subproblem 1
x + -0.0625 = 1.715052842 Simplifying x + -0.0625 = 1.715052842 Reorder the terms: -0.0625 + x = 1.715052842 Solving -0.0625 + x = 1.715052842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 1.715052842 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 1.715052842 + 0.0625 x = 1.715052842 + 0.0625 Combine like terms: 1.715052842 + 0.0625 = 1.777552842 x = 1.777552842 Simplifying x = 1.777552842Subproblem 2
x + -0.0625 = -1.715052842 Simplifying x + -0.0625 = -1.715052842 Reorder the terms: -0.0625 + x = -1.715052842 Solving -0.0625 + x = -1.715052842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -1.715052842 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -1.715052842 + 0.0625 x = -1.715052842 + 0.0625 Combine like terms: -1.715052842 + 0.0625 = -1.652552842 x = -1.652552842 Simplifying x = -1.652552842Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.777552842, -1.652552842}
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