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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 = 62.390625 43.890625 + -13.25x + x2 = 62.390625 Factor a perfect square on the left side: (x + -6.625)(x + -6.625) = 62.390625 Calculate the square root of the right side: 7.898773639 Break this problem into two subproblems by setting (x + -6.625) equal to 7.898773639 and -7.898773639.Subproblem 1
x + -6.625 = 7.898773639 Simplifying x + -6.625 = 7.898773639 Reorder the terms: -6.625 + x = 7.898773639 Solving -6.625 + x = 7.898773639 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 = 7.898773639 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = 7.898773639 + 6.625 x = 7.898773639 + 6.625 Combine like terms: 7.898773639 + 6.625 = 14.523773639 x = 14.523773639 Simplifying x = 14.523773639Subproblem 2
x + -6.625 = -7.898773639 Simplifying x + -6.625 = -7.898773639 Reorder the terms: -6.625 + x = -7.898773639 Solving -6.625 + x = -7.898773639 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 = -7.898773639 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = -7.898773639 + 6.625 x = -7.898773639 + 6.625 Combine like terms: -7.898773639 + 6.625 = -1.273773639 x = -1.273773639 Simplifying x = -1.273773639Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.523773639, -1.273773639}
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