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Simplifying 4x2 + -33x + 33 = -9 + 6 Reorder the terms: 33 + -33x + 4x2 = -9 + 6 Combine like terms: -9 + 6 = -3 33 + -33x + 4x2 = -3 Solving 33 + -33x + 4x2 = -3 Solving for variable 'x'. Reorder the terms: 33 + 3 + -33x + 4x2 = -3 + 3 Combine like terms: 33 + 3 = 36 36 + -33x + 4x2 = -3 + 3 Combine like terms: -3 + 3 = 0 36 + -33x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9 + -8.25x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8.25x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -8.25x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8.25x + x2 = 0 + -9 -8.25x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8.25x + x2 = -9 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 = -9 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -9 + 17.015625 Combine like terms: -9 + 17.015625 = 8.015625 17.015625 + -8.25x + x2 = 8.015625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 8.015625 Calculate the square root of the right side: 2.831187913 Break this problem into two subproblems by setting (x + -4.125) equal to 2.831187913 and -2.831187913.Subproblem 1
x + -4.125 = 2.831187913 Simplifying x + -4.125 = 2.831187913 Reorder the terms: -4.125 + x = 2.831187913 Solving -4.125 + x = 2.831187913 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 = 2.831187913 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 2.831187913 + 4.125 x = 2.831187913 + 4.125 Combine like terms: 2.831187913 + 4.125 = 6.956187913 x = 6.956187913 Simplifying x = 6.956187913Subproblem 2
x + -4.125 = -2.831187913 Simplifying x + -4.125 = -2.831187913 Reorder the terms: -4.125 + x = -2.831187913 Solving -4.125 + x = -2.831187913 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 = -2.831187913 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -2.831187913 + 4.125 x = -2.831187913 + 4.125 Combine like terms: -2.831187913 + 4.125 = 1.293812087 x = 1.293812087 Simplifying x = 1.293812087Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.956187913, 1.293812087}
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