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Simplifying 4x2 + -33x + -54 = 0 Reorder the terms: -54 + -33x + 4x2 = 0 Solving -54 + -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'. -13.5 + -8.25x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -8.25x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -8.25x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -8.25x + x2 = 0 + 13.5 -8.25x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -8.25x + x2 = 13.5 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 = 13.5 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = 13.5 + 17.015625 Combine like terms: 13.5 + 17.015625 = 30.515625 17.015625 + -8.25x + x2 = 30.515625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 30.515625 Calculate the square root of the right side: 5.524094948 Break this problem into two subproblems by setting (x + -4.125) equal to 5.524094948 and -5.524094948.Subproblem 1
x + -4.125 = 5.524094948 Simplifying x + -4.125 = 5.524094948 Reorder the terms: -4.125 + x = 5.524094948 Solving -4.125 + x = 5.524094948 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 = 5.524094948 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 5.524094948 + 4.125 x = 5.524094948 + 4.125 Combine like terms: 5.524094948 + 4.125 = 9.649094948 x = 9.649094948 Simplifying x = 9.649094948Subproblem 2
x + -4.125 = -5.524094948 Simplifying x + -4.125 = -5.524094948 Reorder the terms: -4.125 + x = -5.524094948 Solving -4.125 + x = -5.524094948 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 = -5.524094948 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -5.524094948 + 4.125 x = -5.524094948 + 4.125 Combine like terms: -5.524094948 + 4.125 = -1.399094948 x = -1.399094948 Simplifying x = -1.399094948Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.649094948, -1.399094948}
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