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Simplifying 0 = 4x2 + -53x + 74 Reorder the terms: 0 = 74 + -53x + 4x2 Solving 0 = 74 + -53x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -74 = -74 -74 + 53x + -4x2 = 74 + -53x + 4x2 + -74 + 53x + -4x2 Reorder the terms: -74 + 53x + -4x2 = 74 + -74 + -53x + 53x + 4x2 + -4x2 Combine like terms: 74 + -74 = 0 -74 + 53x + -4x2 = 0 + -53x + 53x + 4x2 + -4x2 -74 + 53x + -4x2 = -53x + 53x + 4x2 + -4x2 Combine like terms: -53x + 53x = 0 -74 + 53x + -4x2 = 0 + 4x2 + -4x2 -74 + 53x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -74 + 53x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 18.5 + -13.25x + x2 = 0 Move the constant term to the right: Add '-18.5' to each side of the equation. 18.5 + -13.25x + -18.5 + x2 = 0 + -18.5 Reorder the terms: 18.5 + -18.5 + -13.25x + x2 = 0 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + -13.25x + x2 = 0 + -18.5 -13.25x + x2 = 0 + -18.5 Combine like terms: 0 + -18.5 = -18.5 -13.25x + x2 = -18.5 The x term is -13.25x. Take half its coefficient (-6.625). Square it (43.890625) and add it to both sides. Add '43.890625' to each side of the equation. -13.25x + 43.890625 + x2 = -18.5 + 43.890625 Reorder the terms: 43.890625 + -13.25x + x2 = -18.5 + 43.890625 Combine like terms: -18.5 + 43.890625 = 25.390625 43.890625 + -13.25x + x2 = 25.390625 Factor a perfect square on the left side: (x + -6.625)(x + -6.625) = 25.390625 Calculate the square root of the right side: 5.038911093 Break this problem into two subproblems by setting (x + -6.625) equal to 5.038911093 and -5.038911093.Subproblem 1
x + -6.625 = 5.038911093 Simplifying x + -6.625 = 5.038911093 Reorder the terms: -6.625 + x = 5.038911093 Solving -6.625 + x = 5.038911093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = 5.038911093 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = 5.038911093 + 6.625 x = 5.038911093 + 6.625 Combine like terms: 5.038911093 + 6.625 = 11.663911093 x = 11.663911093 Simplifying x = 11.663911093Subproblem 2
x + -6.625 = -5.038911093 Simplifying x + -6.625 = -5.038911093 Reorder the terms: -6.625 + x = -5.038911093 Solving -6.625 + x = -5.038911093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = -5.038911093 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = -5.038911093 + 6.625 x = -5.038911093 + 6.625 Combine like terms: -5.038911093 + 6.625 = 1.586088907 x = 1.586088907 Simplifying x = 1.586088907Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.663911093, 1.586088907}
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