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Simplifying 3x2 + -24x + 51 = 0 Reorder the terms: 51 + -24x + 3x2 = 0 Solving 51 + -24x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(17 + -8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(17 + -8x + x2)' equal to zero and attempt to solve: Simplifying 17 + -8x + x2 = 0 Solving 17 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -8x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -8x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -8x + x2 = 0 + -17 -8x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -8x + x2 = -17 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -17 + 16 Reorder the terms: 16 + -8x + x2 = -17 + 16 Combine like terms: -17 + 16 = -1 16 + -8x + x2 = -1 Factor a perfect square on the left side: (x + -4)(x + -4) = -1 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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