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Simplifying 4x2 + -33x + -63 = 0 Reorder the terms: -63 + -33x + 4x2 = 0 Solving -63 + -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'. -15.75 + -8.25x + x2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -8.25x + 15.75 + x2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + -8.25x + x2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -8.25x + x2 = 0 + 15.75 -8.25x + x2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 -8.25x + x2 = 15.75 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 = 15.75 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = 15.75 + 17.015625 Combine like terms: 15.75 + 17.015625 = 32.765625 17.015625 + -8.25x + x2 = 32.765625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 32.765625 Calculate the square root of the right side: 5.724126571 Break this problem into two subproblems by setting (x + -4.125) equal to 5.724126571 and -5.724126571.Subproblem 1
x + -4.125 = 5.724126571 Simplifying x + -4.125 = 5.724126571 Reorder the terms: -4.125 + x = 5.724126571 Solving -4.125 + x = 5.724126571 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 = 5.724126571 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 5.724126571 + 4.125 x = 5.724126571 + 4.125 Combine like terms: 5.724126571 + 4.125 = 9.849126571 x = 9.849126571 Simplifying x = 9.849126571Subproblem 2
x + -4.125 = -5.724126571 Simplifying x + -4.125 = -5.724126571 Reorder the terms: -4.125 + x = -5.724126571 Solving -4.125 + x = -5.724126571 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 = -5.724126571 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -5.724126571 + 4.125 x = -5.724126571 + 4.125 Combine like terms: -5.724126571 + 4.125 = -1.599126571 x = -1.599126571 Simplifying x = -1.599126571Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.849126571, -1.599126571}
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