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Simplifying 8x2 + -27x + 8 = 0 Reorder the terms: 8 + -27x + 8x2 = 0 Solving 8 + -27x + 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 + -3.375x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.375x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -3.375x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.375x + x2 = 0 + -1 -3.375x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.375x + x2 = -1 The x term is -3.375x. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375x + 2.84765625 + x2 = -1 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = -1 + 2.84765625 Combine like terms: -1 + 2.84765625 = 1.84765625 2.84765625 + -3.375x + x2 = 1.84765625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 1.84765625 Calculate the square root of the right side: 1.359285198 Break this problem into two subproblems by setting (x + -1.6875) equal to 1.359285198 and -1.359285198.Subproblem 1
x + -1.6875 = 1.359285198 Simplifying x + -1.6875 = 1.359285198 Reorder the terms: -1.6875 + x = 1.359285198 Solving -1.6875 + x = 1.359285198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = 1.359285198 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 1.359285198 + 1.6875 x = 1.359285198 + 1.6875 Combine like terms: 1.359285198 + 1.6875 = 3.046785198 x = 3.046785198 Simplifying x = 3.046785198Subproblem 2
x + -1.6875 = -1.359285198 Simplifying x + -1.6875 = -1.359285198 Reorder the terms: -1.6875 + x = -1.359285198 Solving -1.6875 + x = -1.359285198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = -1.359285198 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -1.359285198 + 1.6875 x = -1.359285198 + 1.6875 Combine like terms: -1.359285198 + 1.6875 = 0.328214802 x = 0.328214802 Simplifying x = 0.328214802Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.046785198, 0.328214802}
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