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Simplifying 4x2 + -33x + -49 = -4x + 4 Reorder the terms: -49 + -33x + 4x2 = -4x + 4 Reorder the terms: -49 + -33x + 4x2 = 4 + -4x Solving -49 + -33x + 4x2 = 4 + -4x Solving for variable 'x'. Reorder the terms: -49 + -4 + -33x + 4x + 4x2 = 4 + -4x + -4 + 4x Combine like terms: -49 + -4 = -53 -53 + -33x + 4x + 4x2 = 4 + -4x + -4 + 4x Combine like terms: -33x + 4x = -29x -53 + -29x + 4x2 = 4 + -4x + -4 + 4x Reorder the terms: -53 + -29x + 4x2 = 4 + -4 + -4x + 4x Combine like terms: 4 + -4 = 0 -53 + -29x + 4x2 = 0 + -4x + 4x -53 + -29x + 4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -53 + -29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.25 + -7.25x + x2 = 0 Move the constant term to the right: Add '13.25' to each side of the equation. -13.25 + -7.25x + 13.25 + x2 = 0 + 13.25 Reorder the terms: -13.25 + 13.25 + -7.25x + x2 = 0 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + -7.25x + x2 = 0 + 13.25 -7.25x + x2 = 0 + 13.25 Combine like terms: 0 + 13.25 = 13.25 -7.25x + x2 = 13.25 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = 13.25 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 13.25 + 13.140625 Combine like terms: 13.25 + 13.140625 = 26.390625 13.140625 + -7.25x + x2 = 26.390625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 26.390625 Calculate the square root of the right side: 5.137180647 Break this problem into two subproblems by setting (x + -3.625) equal to 5.137180647 and -5.137180647.Subproblem 1
x + -3.625 = 5.137180647 Simplifying x + -3.625 = 5.137180647 Reorder the terms: -3.625 + x = 5.137180647 Solving -3.625 + x = 5.137180647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 5.137180647 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 5.137180647 + 3.625 x = 5.137180647 + 3.625 Combine like terms: 5.137180647 + 3.625 = 8.762180647 x = 8.762180647 Simplifying x = 8.762180647Subproblem 2
x + -3.625 = -5.137180647 Simplifying x + -3.625 = -5.137180647 Reorder the terms: -3.625 + x = -5.137180647 Solving -3.625 + x = -5.137180647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -5.137180647 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -5.137180647 + 3.625 x = -5.137180647 + 3.625 Combine like terms: -5.137180647 + 3.625 = -1.512180647 x = -1.512180647 Simplifying x = -1.512180647Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.762180647, -1.512180647}
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