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Simplifying 8x2 + -27x + 4 = 0 Reorder the terms: 4 + -27x + 8x2 = 0 Solving 4 + -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'. 0.5 + -3.375x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.375x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.375x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.375x + x2 = 0 + -0.5 -3.375x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.375x + x2 = -0.5 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 = -0.5 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = -0.5 + 2.84765625 Combine like terms: -0.5 + 2.84765625 = 2.34765625 2.84765625 + -3.375x + x2 = 2.34765625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 2.34765625 Calculate the square root of the right side: 1.532206334 Break this problem into two subproblems by setting (x + -1.6875) equal to 1.532206334 and -1.532206334.Subproblem 1
x + -1.6875 = 1.532206334 Simplifying x + -1.6875 = 1.532206334 Reorder the terms: -1.6875 + x = 1.532206334 Solving -1.6875 + x = 1.532206334 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 = 1.532206334 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 1.532206334 + 1.6875 x = 1.532206334 + 1.6875 Combine like terms: 1.532206334 + 1.6875 = 3.219706334 x = 3.219706334 Simplifying x = 3.219706334Subproblem 2
x + -1.6875 = -1.532206334 Simplifying x + -1.6875 = -1.532206334 Reorder the terms: -1.6875 + x = -1.532206334 Solving -1.6875 + x = -1.532206334 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 = -1.532206334 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -1.532206334 + 1.6875 x = -1.532206334 + 1.6875 Combine like terms: -1.532206334 + 1.6875 = 0.155293666 x = 0.155293666 Simplifying x = 0.155293666Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.219706334, 0.155293666}
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