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Simplifying 7x + -38 = 4x2 + 52x + 169 Reorder the terms: -38 + 7x = 4x2 + 52x + 169 Reorder the terms: -38 + 7x = 169 + 52x + 4x2 Solving -38 + 7x = 169 + 52x + 4x2 Solving for variable 'x'. Reorder the terms: -38 + -169 + 7x + -52x + -4x2 = 169 + 52x + 4x2 + -169 + -52x + -4x2 Combine like terms: -38 + -169 = -207 -207 + 7x + -52x + -4x2 = 169 + 52x + 4x2 + -169 + -52x + -4x2 Combine like terms: 7x + -52x = -45x -207 + -45x + -4x2 = 169 + 52x + 4x2 + -169 + -52x + -4x2 Reorder the terms: -207 + -45x + -4x2 = 169 + -169 + 52x + -52x + 4x2 + -4x2 Combine like terms: 169 + -169 = 0 -207 + -45x + -4x2 = 0 + 52x + -52x + 4x2 + -4x2 -207 + -45x + -4x2 = 52x + -52x + 4x2 + -4x2 Combine like terms: 52x + -52x = 0 -207 + -45x + -4x2 = 0 + 4x2 + -4x2 -207 + -45x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -207 + -45x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(207 + 45x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(207 + 45x + 4x2)' equal to zero and attempt to solve: Simplifying 207 + 45x + 4x2 = 0 Solving 207 + 45x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 51.75 + 11.25x + x2 = 0 Move the constant term to the right: Add '-51.75' to each side of the equation. 51.75 + 11.25x + -51.75 + x2 = 0 + -51.75 Reorder the terms: 51.75 + -51.75 + 11.25x + x2 = 0 + -51.75 Combine like terms: 51.75 + -51.75 = 0.00 0.00 + 11.25x + x2 = 0 + -51.75 11.25x + x2 = 0 + -51.75 Combine like terms: 0 + -51.75 = -51.75 11.25x + x2 = -51.75 The x term is 11.25x. Take half its coefficient (5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. 11.25x + 31.640625 + x2 = -51.75 + 31.640625 Reorder the terms: 31.640625 + 11.25x + x2 = -51.75 + 31.640625 Combine like terms: -51.75 + 31.640625 = -20.109375 31.640625 + 11.25x + x2 = -20.109375 Factor a perfect square on the left side: (x + 5.625)(x + 5.625) = -20.109375 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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