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Simplifying 4x2 + -33x + -80 = 0 Reorder the terms: -80 + -33x + 4x2 = 0 Solving -80 + -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'. -20 + -8.25x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -8.25x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -8.25x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -8.25x + x2 = 0 + 20 -8.25x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -8.25x + x2 = 20 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 = 20 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = 20 + 17.015625 Combine like terms: 20 + 17.015625 = 37.015625 17.015625 + -8.25x + x2 = 37.015625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 37.015625 Calculate the square root of the right side: 6.084046762 Break this problem into two subproblems by setting (x + -4.125) equal to 6.084046762 and -6.084046762.Subproblem 1
x + -4.125 = 6.084046762 Simplifying x + -4.125 = 6.084046762 Reorder the terms: -4.125 + x = 6.084046762 Solving -4.125 + x = 6.084046762 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 = 6.084046762 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 6.084046762 + 4.125 x = 6.084046762 + 4.125 Combine like terms: 6.084046762 + 4.125 = 10.209046762 x = 10.209046762 Simplifying x = 10.209046762Subproblem 2
x + -4.125 = -6.084046762 Simplifying x + -4.125 = -6.084046762 Reorder the terms: -4.125 + x = -6.084046762 Solving -4.125 + x = -6.084046762 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 = -6.084046762 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -6.084046762 + 4.125 x = -6.084046762 + 4.125 Combine like terms: -6.084046762 + 4.125 = -1.959046762 x = -1.959046762 Simplifying x = -1.959046762Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.209046762, -1.959046762}
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