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Simplifying 4x2 + -33x + 27 = 0 Reorder the terms: 27 + -33x + 4x2 = 0 Solving 27 + -33x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.75 + -8.25x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -8.25x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -8.25x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -8.25x + x2 = 0 + -6.75 -8.25x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -8.25x + x2 = -6.75 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = -6.75 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -6.75 + 17.015625 Combine like terms: -6.75 + 17.015625 = 10.265625 17.015625 + -8.25x + x2 = 10.265625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (x + -4.125) equal to 3.204001404 and -3.204001404.Subproblem 1
x + -4.125 = 3.204001404 Simplifying x + -4.125 = 3.204001404 Reorder the terms: -4.125 + x = 3.204001404 Solving -4.125 + x = 3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 3.204001404 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 3.204001404 + 4.125 x = 3.204001404 + 4.125 Combine like terms: 3.204001404 + 4.125 = 7.329001404 x = 7.329001404 Simplifying x = 7.329001404Subproblem 2
x + -4.125 = -3.204001404 Simplifying x + -4.125 = -3.204001404 Reorder the terms: -4.125 + x = -3.204001404 Solving -4.125 + x = -3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -3.204001404 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -3.204001404 + 4.125 x = -3.204001404 + 4.125 Combine like terms: -3.204001404 + 4.125 = 0.920998596 x = 0.920998596 Simplifying x = 0.920998596Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.329001404, 0.920998596}
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