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Simplifying 8x2 + -33x + -68 = 0 Reorder the terms: -68 + -33x + 8x2 = 0 Solving -68 + -33x + 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'. -8.5 + -4.125x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -4.125x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -4.125x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -4.125x + x2 = 0 + 8.5 -4.125x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -4.125x + x2 = 8.5 The x term is -4.125x. Take half its coefficient (-2.0625). Square it (4.25390625) and add it to both sides. Add '4.25390625' to each side of the equation. -4.125x + 4.25390625 + x2 = 8.5 + 4.25390625 Reorder the terms: 4.25390625 + -4.125x + x2 = 8.5 + 4.25390625 Combine like terms: 8.5 + 4.25390625 = 12.75390625 4.25390625 + -4.125x + x2 = 12.75390625 Factor a perfect square on the left side: (x + -2.0625)(x + -2.0625) = 12.75390625 Calculate the square root of the right side: 3.571261157 Break this problem into two subproblems by setting (x + -2.0625) equal to 3.571261157 and -3.571261157.Subproblem 1
x + -2.0625 = 3.571261157 Simplifying x + -2.0625 = 3.571261157 Reorder the terms: -2.0625 + x = 3.571261157 Solving -2.0625 + x = 3.571261157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = 3.571261157 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = 3.571261157 + 2.0625 x = 3.571261157 + 2.0625 Combine like terms: 3.571261157 + 2.0625 = 5.633761157 x = 5.633761157 Simplifying x = 5.633761157Subproblem 2
x + -2.0625 = -3.571261157 Simplifying x + -2.0625 = -3.571261157 Reorder the terms: -2.0625 + x = -3.571261157 Solving -2.0625 + x = -3.571261157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = -3.571261157 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = -3.571261157 + 2.0625 x = -3.571261157 + 2.0625 Combine like terms: -3.571261157 + 2.0625 = -1.508761157 x = -1.508761157 Simplifying x = -1.508761157Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.633761157, -1.508761157}
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