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Simplifying 8x2 + -1x + -194 = 0 Reorder the terms: -194 + -1x + 8x2 = 0 Solving -194 + -1x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -24.25 + -0.125x + x2 = 0 Move the constant term to the right: Add '24.25' to each side of the equation. -24.25 + -0.125x + 24.25 + x2 = 0 + 24.25 Reorder the terms: -24.25 + 24.25 + -0.125x + x2 = 0 + 24.25 Combine like terms: -24.25 + 24.25 = 0.00 0.00 + -0.125x + x2 = 0 + 24.25 -0.125x + x2 = 0 + 24.25 Combine like terms: 0 + 24.25 = 24.25 -0.125x + x2 = 24.25 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 = 24.25 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 24.25 + 0.00390625 Combine like terms: 24.25 + 0.00390625 = 24.25390625 0.00390625 + -0.125x + x2 = 24.25390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 24.25390625 Calculate the square root of the right side: 4.924825505 Break this problem into two subproblems by setting (x + -0.0625) equal to 4.924825505 and -4.924825505.Subproblem 1
x + -0.0625 = 4.924825505 Simplifying x + -0.0625 = 4.924825505 Reorder the terms: -0.0625 + x = 4.924825505 Solving -0.0625 + x = 4.924825505 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 = 4.924825505 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 4.924825505 + 0.0625 x = 4.924825505 + 0.0625 Combine like terms: 4.924825505 + 0.0625 = 4.987325505 x = 4.987325505 Simplifying x = 4.987325505Subproblem 2
x + -0.0625 = -4.924825505 Simplifying x + -0.0625 = -4.924825505 Reorder the terms: -0.0625 + x = -4.924825505 Solving -0.0625 + x = -4.924825505 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 = -4.924825505 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -4.924825505 + 0.0625 x = -4.924825505 + 0.0625 Combine like terms: -4.924825505 + 0.0625 = -4.862325505 x = -4.862325505 Simplifying x = -4.862325505Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.987325505, -4.862325505}
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