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Simplifying -8x2 + -124x + -352 = -5x2 + -79x + 184 Reorder the terms: -352 + -124x + -8x2 = -5x2 + -79x + 184 Reorder the terms: -352 + -124x + -8x2 = 184 + -79x + -5x2 Solving -352 + -124x + -8x2 = 184 + -79x + -5x2 Solving for variable 'x'. Reorder the terms: -352 + -184 + -124x + 79x + -8x2 + 5x2 = 184 + -79x + -5x2 + -184 + 79x + 5x2 Combine like terms: -352 + -184 = -536 -536 + -124x + 79x + -8x2 + 5x2 = 184 + -79x + -5x2 + -184 + 79x + 5x2 Combine like terms: -124x + 79x = -45x -536 + -45x + -8x2 + 5x2 = 184 + -79x + -5x2 + -184 + 79x + 5x2 Combine like terms: -8x2 + 5x2 = -3x2 -536 + -45x + -3x2 = 184 + -79x + -5x2 + -184 + 79x + 5x2 Reorder the terms: -536 + -45x + -3x2 = 184 + -184 + -79x + 79x + -5x2 + 5x2 Combine like terms: 184 + -184 = 0 -536 + -45x + -3x2 = 0 + -79x + 79x + -5x2 + 5x2 -536 + -45x + -3x2 = -79x + 79x + -5x2 + 5x2 Combine like terms: -79x + 79x = 0 -536 + -45x + -3x2 = 0 + -5x2 + 5x2 -536 + -45x + -3x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -536 + -45x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(536 + 45x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(536 + 45x + 3x2)' equal to zero and attempt to solve: Simplifying 536 + 45x + 3x2 = 0 Solving 536 + 45x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 178.6666667 + 15x + x2 = 0 Move the constant term to the right: Add '-178.6666667' to each side of the equation. 178.6666667 + 15x + -178.6666667 + x2 = 0 + -178.6666667 Reorder the terms: 178.6666667 + -178.6666667 + 15x + x2 = 0 + -178.6666667 Combine like terms: 178.6666667 + -178.6666667 = 0.0000000 0.0000000 + 15x + x2 = 0 + -178.6666667 15x + x2 = 0 + -178.6666667 Combine like terms: 0 + -178.6666667 = -178.6666667 15x + x2 = -178.6666667 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -178.6666667 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -178.6666667 + 56.25 Combine like terms: -178.6666667 + 56.25 = -122.4166667 56.25 + 15x + x2 = -122.4166667 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = -122.4166667 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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