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Simplifying 6x2 + -17x + 30 = 4x + 3 Reorder the terms: 30 + -17x + 6x2 = 4x + 3 Reorder the terms: 30 + -17x + 6x2 = 3 + 4x Solving 30 + -17x + 6x2 = 3 + 4x Solving for variable 'x'. Reorder the terms: 30 + -3 + -17x + -4x + 6x2 = 3 + 4x + -3 + -4x Combine like terms: 30 + -3 = 27 27 + -17x + -4x + 6x2 = 3 + 4x + -3 + -4x Combine like terms: -17x + -4x = -21x 27 + -21x + 6x2 = 3 + 4x + -3 + -4x Reorder the terms: 27 + -21x + 6x2 = 3 + -3 + 4x + -4x Combine like terms: 3 + -3 = 0 27 + -21x + 6x2 = 0 + 4x + -4x 27 + -21x + 6x2 = 4x + -4x Combine like terms: 4x + -4x = 0 27 + -21x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -7x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -7x + 2x2 = 0 Solving 9 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -3.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -3.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -3.5x + x2 = 0 + -4.5 -3.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -3.5x + x2 = -4.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -4.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -4.5 + 3.0625 Combine like terms: -4.5 + 3.0625 = -1.4375 3.0625 + -3.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -1.4375 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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