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Simplifying 8x2 + 33x + 8 = 0 Reorder the terms: 8 + 33x + 8x2 = 0 Solving 8 + 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'. 1 + 4.125x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.125x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4.125x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.125x + x2 = 0 + -1 4.125x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.125x + x2 = -1 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 = -1 + 4.25390625 Reorder the terms: 4.25390625 + 4.125x + x2 = -1 + 4.25390625 Combine like terms: -1 + 4.25390625 = 3.25390625 4.25390625 + 4.125x + x2 = 3.25390625 Factor a perfect square on the left side: (x + 2.0625)(x + 2.0625) = 3.25390625 Calculate the square root of the right side: 1.803858711 Break this problem into two subproblems by setting (x + 2.0625) equal to 1.803858711 and -1.803858711.Subproblem 1
x + 2.0625 = 1.803858711 Simplifying x + 2.0625 = 1.803858711 Reorder the terms: 2.0625 + x = 1.803858711 Solving 2.0625 + x = 1.803858711 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 = 1.803858711 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = 1.803858711 + -2.0625 x = 1.803858711 + -2.0625 Combine like terms: 1.803858711 + -2.0625 = -0.258641289 x = -0.258641289 Simplifying x = -0.258641289Subproblem 2
x + 2.0625 = -1.803858711 Simplifying x + 2.0625 = -1.803858711 Reorder the terms: 2.0625 + x = -1.803858711 Solving 2.0625 + x = -1.803858711 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 = -1.803858711 + -2.0625 Combine like terms: 2.0625 + -2.0625 = 0.0000 0.0000 + x = -1.803858711 + -2.0625 x = -1.803858711 + -2.0625 Combine like terms: -1.803858711 + -2.0625 = -3.866358711 x = -3.866358711 Simplifying x = -3.866358711Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.258641289, -3.866358711}
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