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Simplifying 7x + -38 = 4x2 + 60x + 225 Reorder the terms: -38 + 7x = 4x2 + 60x + 225 Reorder the terms: -38 + 7x = 225 + 60x + 4x2 Solving -38 + 7x = 225 + 60x + 4x2 Solving for variable 'x'. Reorder the terms: -38 + -225 + 7x + -60x + -4x2 = 225 + 60x + 4x2 + -225 + -60x + -4x2 Combine like terms: -38 + -225 = -263 -263 + 7x + -60x + -4x2 = 225 + 60x + 4x2 + -225 + -60x + -4x2 Combine like terms: 7x + -60x = -53x -263 + -53x + -4x2 = 225 + 60x + 4x2 + -225 + -60x + -4x2 Reorder the terms: -263 + -53x + -4x2 = 225 + -225 + 60x + -60x + 4x2 + -4x2 Combine like terms: 225 + -225 = 0 -263 + -53x + -4x2 = 0 + 60x + -60x + 4x2 + -4x2 -263 + -53x + -4x2 = 60x + -60x + 4x2 + -4x2 Combine like terms: 60x + -60x = 0 -263 + -53x + -4x2 = 0 + 4x2 + -4x2 -263 + -53x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -263 + -53x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(263 + 53x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(263 + 53x + 4x2)' equal to zero and attempt to solve: Simplifying 263 + 53x + 4x2 = 0 Solving 263 + 53x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 65.75 + 13.25x + x2 = 0 Move the constant term to the right: Add '-65.75' to each side of the equation. 65.75 + 13.25x + -65.75 + x2 = 0 + -65.75 Reorder the terms: 65.75 + -65.75 + 13.25x + x2 = 0 + -65.75 Combine like terms: 65.75 + -65.75 = 0.00 0.00 + 13.25x + x2 = 0 + -65.75 13.25x + x2 = 0 + -65.75 Combine like terms: 0 + -65.75 = -65.75 13.25x + x2 = -65.75 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 = -65.75 + 43.890625 Reorder the terms: 43.890625 + 13.25x + x2 = -65.75 + 43.890625 Combine like terms: -65.75 + 43.890625 = -21.859375 43.890625 + 13.25x + x2 = -21.859375 Factor a perfect square on the left side: (x + 6.625)(x + 6.625) = -21.859375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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